[{"publication":"Symmetry, Integrability and Geometry: Methods and Applications","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","arxiv":1,"fulldoi":"https://doi.org/10.3842/SIGMA.2026.024","oa":1,"date_published":"2026-03-14T00:00:00Z","date_created":"2026-04-12T22:01:51Z","type":"journal_article","intvolume":"        22","status":"public","year":"2026","day":"14","author":[{"first_name":"Nhok T","full_name":"Ngo, Nhok T","id":"28e53c8c-896a-11ed-bdf8-f809043ce2f0","last_name":"Ngo"}],"OA_place":"publisher","volume":22,"quality_controlled":"1","file":[{"success":1,"content_type":"application/pdf","file_id":"21740","creator":"dernst","file_size":975460,"file_name":"2026_SIGMA_Ngo.pdf","access_level":"open_access","date_created":"2026-04-16T06:06:54Z","checksum":"29b28b5f8717ed1a084a2b551d0fd284","date_updated":"2026-04-16T06:06:54Z","relation":"main_file"}],"article_type":"original","OA_type":"diamond","has_accepted_license":"1","department":[{"_id":"TaHa"}],"corr_author":"1","doi":"10.3842/SIGMA.2026.024","file_date_updated":"2026-04-16T06:06:54Z","citation":{"mla":"Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix Space.” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>, vol. 22, 024, National Academy of Science of Ukraine, 2026, doi:<a href=\"https://doi.org/10.3842/SIGMA.2026.024\">10.3842/SIGMA.2026.024</a>.","apa":"Ngo, N. T. (2026). Big algebra in type A for the coordinate ring of the matrix space. <i>Symmetry, Integrability and Geometry: Methods and Applications</i>. National Academy of Science of Ukraine. <a href=\"https://doi.org/10.3842/SIGMA.2026.024\">https://doi.org/10.3842/SIGMA.2026.024</a>","short":"N.T. Ngo, Symmetry, Integrability and Geometry: Methods and Applications 22 (2026).","chicago":"Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix Space.” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>. National Academy of Science of Ukraine, 2026. <a href=\"https://doi.org/10.3842/SIGMA.2026.024\">https://doi.org/10.3842/SIGMA.2026.024</a>.","ama":"Ngo NT. Big algebra in type A for the coordinate ring of the matrix space. <i>Symmetry, Integrability and Geometry: Methods and Applications</i>. 2026;22. doi:<a href=\"https://doi.org/10.3842/SIGMA.2026.024\">10.3842/SIGMA.2026.024</a>","ieee":"N. T. Ngo, “Big algebra in type A for the coordinate ring of the matrix space,” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>, vol. 22. National Academy of Science of Ukraine, 2026.","ista":"Ngo NT. 2026. Big algebra in type A for the coordinate ring of the matrix space. Symmetry, Integrability and Geometry: Methods and Applications. 22, 024."},"abstract":[{"lang":"eng","text":"In this paper, we consider the big algebra recently introduced by Hausel for the GLn-action on the coordinate ring of the matrix space Mat(n,r). In particular, we obtain explicit formulas for the big algebra generators in terms of differential operators with polynomial coefficients. We show that big algebras in type A are commutative and relate them to the Bethe subalgebra in the Yangian Y(gln). We apply these results to big algebras of symmetric powers of the standard representation of GLn.\r\n."}],"publication_identifier":{"eissn":["1815-0659"]},"DOAJ_listed":"1","article_processing_charge":"No","title":"Big algebra in type A for the coordinate ring of the matrix space","acknowledgement":"I would like to express my gratitude to Tam´as Hausel for introducing me to the subject and\r\nfor his constant guidance throughout this work. I would also like to thank Tam´as Hausel,\r\nMischa Elkner, Jakub L¨owit, Anton Mellit, Marino Romero, Leonid Rybnikov for many fruitful\r\ndiscussions and feedback on earlier drafts of this paper. We are grateful to the anonymous\r\nreferees for many useful comments and suggestions that improved the manuscript. This work was done during the author’s PhD studies at the Institute of Science and Technology Austria (ISTA). The author was supported by the Austrian Science Fund (FWF) grant\r\n“Geometry of the tip of the global nilpotent cone” no. 10.55776/P35847 and the DOC Fellowship of the Austrian Academy of Sciences. The author also acknowledges the long-term program\r\nof support of the Ukrainian research teams at the Polish Academy of Sciences carried out in\r\ncollaboration with the U.S. National Academy of Sciences with the financial support of external\r\npartners. For open access purposes, the author has applied a CC BY public copyright license\r\nto any author-accepted manuscript version arising from this submission.","external_id":{"arxiv":["2501.04605"]},"_id":"21718","publisher":"National Academy of Science of Ukraine","date_updated":"2026-04-16T06:11:12Z","ddc":["510"],"scopus_import":"1","language":[{"iso":"eng"}],"month":"03","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","article_number":"024","project":[{"grant_number":"P35847","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone"},{"name":"Big algebras in classical types","_id":"e6c64f42-ab3c-11f0-94c7-a95658059ccc","grant_number":"27483"}]},{"fulldoi":"https://doi.org/10.1007/s00031-026-09958-y","publication_status":"epub_ahead","arxiv":1,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication":"Transformation Groups","date_created":"2026-03-23T15:10:43Z","date_published":"2026-03-14T00:00:00Z","oa":1,"year":"2026","status":"public","type":"journal_article","author":[{"last_name":"Elkner","id":"477faa59-080d-11ed-979a-c693ab7638ab","full_name":"Elkner, Mischa M","first_name":"Mischa M"}],"day":"14","OA_place":"publisher","das_tickbox":"1","article_type":"original","OA_type":"hybrid","quality_controlled":"1","corr_author":"1","department":[{"_id":"TaHa"}],"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["1531-586X"],"issn":["1083-4362"]},"abstract":[{"text":"We study Kirillov algebras attached to minuscule highest weight representations of semisimple Lie algebras. They can be viewed as equivariant cohomology algebras of partial flag varieties. Real structures on the varieties then induce involutions of these algebras. We describe how these involutions act on the spectra of minuscule Kirillov algebras, and model the fixed points via the equivariant cohomology of real partial flag varieties. We then use this model to characterise freeness of the fixed point coordinate ring over the appropriate base. As an application, we recover a q = -1 phenomenon of Stembridge in the minuscule case by geometric means.","lang":"eng"}],"citation":{"ieee":"M. M. Elkner, “On involutions of minuscule Kirillov algebras induced by real structures,” <i>Transformation Groups</i>. Springer Nature, 2026.","ista":"Elkner MM. 2026. On involutions of minuscule Kirillov algebras induced by real structures. Transformation Groups.","chicago":"Elkner, Mischa M. “On Involutions of Minuscule Kirillov Algebras Induced by Real Structures.” <i>Transformation Groups</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00031-026-09958-y\">https://doi.org/10.1007/s00031-026-09958-y</a>.","short":"M.M. Elkner, Transformation Groups (2026).","ama":"Elkner MM. On involutions of minuscule Kirillov algebras induced by real structures. <i>Transformation Groups</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s00031-026-09958-y\">10.1007/s00031-026-09958-y</a>","mla":"Elkner, Mischa M. “On Involutions of Minuscule Kirillov Algebras Induced by Real Structures.” <i>Transformation Groups</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00031-026-09958-y\">10.1007/s00031-026-09958-y</a>.","apa":"Elkner, M. M. (2026). On involutions of minuscule Kirillov algebras induced by real structures. <i>Transformation Groups</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00031-026-09958-y\">https://doi.org/10.1007/s00031-026-09958-y</a>"},"doi":"10.1007/s00031-026-09958-y","title":"On involutions of minuscule Kirillov algebras induced by real structures","date_updated":"2026-07-22T07:37:35Z","ddc":["510"],"_id":"21489","publisher":"Springer Nature","external_id":{"arxiv":["2411.16270"]},"acknowledgement":"I would like to thank Tamás Hausel for introducing me to this area of mathematics and for his constant guidance. I would also like to thank Jakub Löwit and Miguel González for fruitful discussions and many helpful comments on this paper. This work was done during the author’s PhD studies at the Institute of Science and Technology Austria (ISTA). It was funded by the Austrian Science Fund (FWF) 10.55776/P35847. Open access funding provided by Institute of Science and Technology (IST Austria). ","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00031-026-09958-y"}],"oa_version":"Published Version","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}]},{"article_processing_charge":"No","publisher_comment":"For open access purposes, the author has applied a CC BY public copyright\r\nlicense to any author-accepted manuscript version arising from this submission.","doi":"10.15479/AT-ISTA-22694","file_date_updated":"2026-08-14T11:42:42Z","citation":{"ama":"Löwit J. Equivariant K-theory of affine Grassmannians in representation theory and arithmetic. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22694\">10.15479/AT-ISTA-22694</a>","short":"J. Löwit, Equivariant K-Theory of Affine Grassmannians in Representation Theory and Arithmetic, Institute of Science and Technology Austria, 2026.","chicago":"Löwit, Jakub. “Equivariant K-Theory of Affine Grassmannians in Representation Theory and Arithmetic.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-22694\">https://doi.org/10.15479/AT-ISTA-22694</a>.","ista":"Löwit J. 2026. Equivariant K-theory of affine Grassmannians in representation theory and arithmetic. Institute of Science and Technology Austria.","ieee":"J. Löwit, “Equivariant K-theory of affine Grassmannians in representation theory and arithmetic,” Institute of Science and Technology Austria, 2026.","apa":"Löwit, J. (2026). <i>Equivariant K-theory of affine Grassmannians in representation theory and arithmetic</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-22694\">https://doi.org/10.15479/AT-ISTA-22694</a>","mla":"Löwit, Jakub. <i>Equivariant K-Theory of Affine Grassmannians in Representation Theory and Arithmetic</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22694\">10.15479/AT-ISTA-22694</a>."},"publication_identifier":{"issn":["2663-337X"]},"abstract":[{"text":"We develop and employ techniques from equivariant algebraic K-theory and related invariants\r\nin the context of geometric representation theory, in both arithmetic and topological situations.\r\nWe showcase the use of such techniques on the affine Grassmannian Gr, a space of fundamental\r\ninterest in the geometric Langlands program.\r\n\r\nIt is a deep development of mathematics of the last century that many concrete, yet combina-\r\ntorially complex algebraic problems may be effectively studied through the lens of algebraic\r\ngeometry. The objects of interest can be often realized as cohomological invariants of algebraic\r\nvarieties, and good understanding of their geometry sheds light into the original questions.\r\nSuch techniques have seen immense applications in the Langlands program, where they go\r\nunder the label of geometric representation theory.\r\n\r\nOne source of powerful invariants in algebraic geometry comes from algebraic K-theory,\r\nHochschild homology, and their relatives. These localizing invariants contain large amount\r\nof information, but are quite hard to compute. For this reason, their usage in geometric\r\nrepresentation theory has been limited.\r\n\r\nThe aim of this thesis is to showcase how to control such invariants in the situations of\r\ninterest and use them to obtain new insights. We start by reinterpreting equivariant Hochschild\r\nhomology in terms of functions on certain fixed-point schemes, which are of independent\r\ninterest. We compare it to equivariant K-theory via the trace map. We give new computations\r\nand comparisons of such invariants of affine Schubert varieties in Gr, including arithmetic\r\nsituations. We show that they behave much better than expected.\r\n\r\nWe finally utilize this circle of ideas in a purely topological setting. We describe the varying\r\nfixed points of the extended torus action on the affine Grassmannian, and use it to compute\r\nits equivariant topological K-theory ring. The answer is nontrivial and verifies an outstanding\r\nconjecture in the subject.\r\n\r\nWe compare, partly conjecturally, the resulting K-theory ring to the completed center of an\r\nintegral even hybrid quantum group and its deformed quantum category O. This gives a\r\ngenuine application of our computations in pure representation theory.","lang":"eng"}],"corr_author":"1","alternative_title":["ISTA Thesis"],"has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"_id":"22694","publisher":"Institute of Science and Technology Austria","ddc":["510","516","512","514","513"],"date_updated":"2026-08-26T06:53:55Z","acknowledgement":"It was funded by a DOC Fellowship of the Austrian Academy of Sciences entitled Arithmetic,\r\ngeometry, topology and representation theory arising from the affine Grassmannian. It was\r\nfurther funded by the Austrian Science Fund FWF 10.55776/P35847, and an Erasmus+ staff\r\nmobility training. \r\n","degree_awarded":"PhD","title":"Equivariant K-theory of affine Grassmannians in representation theory and arithmetic","oa_version":"Published Version","language":[{"iso":"eng"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"08","project":[{"_id":"901e2a43-16d5-11f0-9cad-9cead34748d6","name":"Arithmetic, geometry, topology and representation theory arising from the affine Grassmannian","grant_number":"27004"},{"name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","grant_number":"P35847"}],"publication_status":"published","fulldoi":"https://doi.org/10.15479/AT-ISTA-22694","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"related_material":{"record":[{"id":"21751","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"22693"}]},"status":"public","year":"2026","type":"dissertation","date_created":"2026-08-12T14:05:36Z","oa":1,"date_published":"2026-08-05T00:00:00Z","OA_place":"publisher","page":"185","doi_confirm":"1","author":[{"full_name":"Löwit, Jakub","first_name":"Jakub","last_name":"Löwit","id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0"}],"day":"05","file":[{"date_created":"2026-08-14T11:42:31Z","access_level":"open_access","file_name":"2026_Löwit_Jakub_Thesis.pdf","relation":"main_file","date_updated":"2026-08-14T11:42:31Z","checksum":"2d0be77791dc296621c6c0f76be9d0d7","content_type":"application/pdf","file_id":"22709","file_size":1574709,"creator":"jloewit"},{"file_size":1085118,"creator":"jloewit","content_type":"application/zip","file_id":"22710","date_updated":"2026-08-14T11:42:42Z","relation":"source_file","checksum":"61bde4b58c1e6c7baeb561e41f82659b","date_created":"2026-08-14T11:42:42Z","access_level":"closed","file_name":"2026_Löwit_Jakub_Source_files.zip"}],"supervisor":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9582-2634","full_name":"Hausel, Tamás","first_name":"Tamás"}]},{"article_type":"original","OA_type":"hybrid","quality_controlled":"1","supplementarymaterial":"no","OA_place":"publisher","das_tickbox":"0","author":[{"full_name":"Löwit, Jakub","first_name":"Jakub","last_name":"Löwit","id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0"}],"day":"26","status":"public","year":"2026","PlanS_conform":"1","researchdata_availability":"no","related_material":{"record":[{"relation":"dissertation_contains","id":"22694","status":"public"}]},"mathsc":["19E08","19L47","20G44","14G17","19D55","14F43","14L30","14D24","14M25"],"type":"journal_article","date_created":"2026-08-12T13:29:17Z","date_published":"2026-03-26T00:00:00Z","oa":1,"fulldoi":"https://doi.org/10.4171/dm/1064","publication_status":"epub_ahead","arxiv":1,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication":"Documenta Mathematica","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"main_file_link":[{"url":"https://doi.org/10.4171/DM/1064","open_access":"1"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","language":[{"iso":"eng"}],"scopus_import":"1","ddc":["500"],"date_updated":"2026-08-26T06:53:54Z","_id":"22693","publisher":"EMS Press","external_id":{"arxiv":["2409.18925"]},"acknowledgement":"I would like to thank the following people for fruitful discussions,\r\nhelpful sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt, Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,\r\nBernhard Köck, Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya\r\nRavi, Kamil Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I\r\nwould further like to thank Marc Hoyois and the anonymous referee for spotting an error\r\nin a previous version.\r\nThis work was done during author’s PhD at the Institute of Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the Austrian Academy\r\nof Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847. For open access\r\npurposes, the author has applied a CC BY public copyright license to any author-accepted\r\nmanuscript version arising from this submission.","title":"Equivariant K-theory, affine Grassmannian and perfection","article_processing_charge":"Yes (in subscription journal)","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"abstract":[{"text":"We study torus-equivariant algebraic K-theory of affine Schubert varieties in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a geometric description in terms of global functions on certain fixed-point schemes. We prove that Fp-linearly, this comparison is an isomorphism. Our approach is quite constructive, resulting in new computations of these K-theory rings. We establish various structural results for equivariant perfect algebraic K-theory on the way; we believe these are of independent interest.","lang":"eng"}],"doi":"10.4171/dm/1064","citation":{"mla":"Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta Mathematica</i>, EMS Press, 2026, doi:<a href=\"https://doi.org/10.4171/dm/1064\">10.4171/dm/1064</a>.","apa":"Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. EMS Press. <a href=\"https://doi.org/10.4171/dm/1064\">https://doi.org/10.4171/dm/1064</a>","chicago":"Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta Mathematica</i>. EMS Press, 2026. <a href=\"https://doi.org/10.4171/dm/1064\">https://doi.org/10.4171/dm/1064</a>.","short":"J. Löwit, Documenta Mathematica (2026).","ama":"Löwit J. Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta Mathematica</i>. 2026. doi:<a href=\"https://doi.org/10.4171/dm/1064\">10.4171/dm/1064</a>","ieee":"J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” <i>Documenta Mathematica</i>. EMS Press, 2026.","ista":"Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica."},"keyword":["equivariant algebraic K-theory","perfection in positive characteristic","affine Grassmannian","affine Schubert varieties","Dennis trace map","equivariant Hochschild homology","fixed-point schemes","toric varieties"],"corr_author":"1","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"has_accepted_license":"1"},{"article_processing_charge":"Yes","DOAJ_listed":"1","doi":"10.46298/epiga.2025.12591","file_date_updated":"2025-02-25T06:53:27Z","citation":{"ieee":"T. Hausel and K. P. Rychlewicz, “Spectrum of equivariant cohomology as a fixed point scheme,” <i>Epijournal de Geometrie Algebrique</i>, vol. 9. EPI Sciences, 2025.","ista":"Hausel T, Rychlewicz KP. 2025. Spectrum of equivariant cohomology as a fixed point scheme. Epijournal de Geometrie Algebrique. 9, 1.","chicago":"Hausel, Tamás, and Kamil P Rychlewicz. “Spectrum of Equivariant Cohomology as a Fixed Point Scheme.” <i>Epijournal de Geometrie Algebrique</i>. EPI Sciences, 2025. <a href=\"https://doi.org/10.46298/epiga.2025.12591\">https://doi.org/10.46298/epiga.2025.12591</a>.","short":"T. Hausel, K.P. Rychlewicz, Epijournal de Geometrie Algebrique 9 (2025).","ama":"Hausel T, Rychlewicz KP. Spectrum of equivariant cohomology as a fixed point scheme. <i>Epijournal de Geometrie Algebrique</i>. 2025;9. doi:<a href=\"https://doi.org/10.46298/epiga.2025.12591\">10.46298/epiga.2025.12591</a>","mla":"Hausel, Tamás, and Kamil P. Rychlewicz. “Spectrum of Equivariant Cohomology as a Fixed Point Scheme.” <i>Epijournal de Geometrie Algebrique</i>, vol. 9, 1, EPI Sciences, 2025, doi:<a href=\"https://doi.org/10.46298/epiga.2025.12591\">10.46298/epiga.2025.12591</a>.","apa":"Hausel, T., &#38; Rychlewicz, K. P. (2025). Spectrum of equivariant cohomology as a fixed point scheme. <i>Epijournal de Geometrie Algebrique</i>. EPI Sciences. <a href=\"https://doi.org/10.46298/epiga.2025.12591\">https://doi.org/10.46298/epiga.2025.12591</a>"},"publication_identifier":{"eissn":["2491-6765"]},"abstract":[{"lang":"eng","text":"An action of a complex reductive group G on a smooth projective variety X is regular when all regular unipotent elements in G act with finitely many fixed points. Then the complex G\r\n-equivariant cohomology ring of X is isomorphic to the coordinate ring of a certain regular fixed point scheme. Examples include partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties. We also show that a more general version of the fixed point scheme allows a generalisation to GKM spaces, such as toric varieties."}],"corr_author":"1","has_accepted_license":"1","department":[{"_id":"TaHa"}],"publisher":"EPI Sciences","_id":"19071","ddc":["510"],"date_updated":"2025-04-15T06:31:58Z","acknowledgement":"The first author was supported by an FWF grant “Geometry of the top of the nilpotent cone” number P 35847. The second author was supported by an Austrian Academy of Sciences DOC Fellowship “Topology of open smooth varieties with a torus action”. ","external_id":{"arxiv":["2212.11836"]},"title":"Spectrum of equivariant cohomology as a fixed point scheme","oa_version":"Published Version","month":"02","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","project":[{"name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","grant_number":"P35847"},{"grant_number":"26525","_id":"34cd0f74-11ca-11ed-8bc3-bf0492a14a24","name":"Topology of open smooth varieties with a torus action"}],"article_number":"1","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.46298/epiga.2025.12591","publication":"Epijournal de Geometrie Algebrique","tmp":{"image":"/images/cc_by_sa.png","short":"CC BY-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)"},"intvolume":"         9","related_material":{"record":[{"id":"17157","relation":"earlier_version","status":"public"}]},"year":"2025","status":"public","type":"journal_article","date_created":"2025-02-23T23:01:56Z","oa":1,"date_published":"2025-02-03T00:00:00Z","OA_place":"publisher","license":"https://creativecommons.org/licenses/by-sa/4.0/","author":[{"orcid":"0000-0002-9582-2634","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","full_name":"Hausel, Tamás"},{"full_name":"Rychlewicz, Kamil P","first_name":"Kamil P","last_name":"Rychlewicz","id":"85A07246-A8BF-11E9-B4FA-D9E3E5697425"}],"day":"03","article_type":"original","OA_type":"gold","quality_controlled":"1","file":[{"access_level":"open_access","date_created":"2025-02-25T06:53:27Z","file_name":"2025_Epiga_Hausel.pdf","checksum":"3915c6f117461502f7103878460428df","date_updated":"2025-02-25T06:53:27Z","relation":"main_file","file_id":"19085","content_type":"application/pdf","success":1,"file_size":3276395,"creator":"dernst"}],"volume":9},{"volume":29,"article_type":"original","OA_type":"hybrid","quality_controlled":"1","file":[{"file_id":"19644","content_type":"application/pdf","success":1,"file_size":424364,"creator":"dernst","access_level":"open_access","date_created":"2025-05-05T06:57:49Z","file_name":"2025_RepresentationTheory_Nessonov.pdf","checksum":"f6541ea1736a7413c6d24f14d64a4dda","relation":"main_file","date_updated":"2025-05-05T06:57:49Z"}],"author":[{"last_name":"Nessonov","first_name":"Nikolay","full_name":"Nessonov, Nikolay"},{"last_name":"Ngo","id":"28e53c8c-896a-11ed-bdf8-f809043ce2f0","full_name":"Ngo, Nhok T","first_name":"Nhok T"}],"day":"10","OA_place":"publisher","page":"256-288","date_created":"2025-04-24T08:48:05Z","oa":1,"date_published":"2025-04-10T00:00:00Z","intvolume":"        29","year":"2025","status":"public","issue":"8","type":"journal_article","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1090/ert/689","publication":"Representation Theory","tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"month":"04","scopus_import":"1","oa_version":"Published Version","title":"Indecomposable characters of inductive limits of symmetric groups","_id":"19621","publisher":"American Mathematical Society","ddc":["510"],"date_updated":"2025-05-05T06:59:07Z","acknowledgement":"The authors were partially supported by the “Long-term program of support of the Ukrainian research teams at the Polish Academy of Sciences carried out in collaboration with the U.S. National Academy of Sciences with the financial support of external partners”. The second author was also supported by the Austrian Science Fund (FWF) grant “Geometry of the tip of the global nilpotent cone” no. 10.55776/P35847","external_id":{"arxiv":["2206.01964"]},"corr_author":"1","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"article_processing_charge":"Yes (in subscription journal)","doi":"10.1090/ert/689","file_date_updated":"2025-05-05T06:57:49Z","citation":{"chicago":"Nessonov, Nikolay, and Nhok T Ngo. “Indecomposable Characters of Inductive Limits of Symmetric Groups.” <i>Representation Theory</i>. American Mathematical Society, 2025. <a href=\"https://doi.org/10.1090/ert/689\">https://doi.org/10.1090/ert/689</a>.","short":"N. Nessonov, N.T. Ngo, Representation Theory 29 (2025) 256–288.","ama":"Nessonov N, Ngo NT. Indecomposable characters of inductive limits of symmetric groups. <i>Representation Theory</i>. 2025;29(8):256-288. doi:<a href=\"https://doi.org/10.1090/ert/689\">10.1090/ert/689</a>","ieee":"N. Nessonov and N. T. Ngo, “Indecomposable characters of inductive limits of symmetric groups,” <i>Representation Theory</i>, vol. 29, no. 8. American Mathematical Society, pp. 256–288, 2025.","ista":"Nessonov N, Ngo NT. 2025. Indecomposable characters of inductive limits of symmetric groups. Representation Theory. 29(8), 256–288.","mla":"Nessonov, Nikolay, and Nhok T. Ngo. “Indecomposable Characters of Inductive Limits of Symmetric Groups.” <i>Representation Theory</i>, vol. 29, no. 8, American Mathematical Society, 2025, pp. 256–88, doi:<a href=\"https://doi.org/10.1090/ert/689\">10.1090/ert/689</a>.","apa":"Nessonov, N., &#38; Ngo, N. T. (2025). Indecomposable characters of inductive limits of symmetric groups. <i>Representation Theory</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/ert/689\">https://doi.org/10.1090/ert/689</a>"},"abstract":[{"text":"In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of inductive limits of the symmetric groups under block diagonal embedding. As a corollary we obtain the full classification of the isomorphism classes of these inductive limits.","lang":"eng"}],"publication_identifier":{"issn":["1088-4165"]}},{"APC_amount":"2742,92 EUR","external_id":{"pmid":["39259592"]},"acknowledgement":"We thank Nigel Hitchin for discussions and the joint projects this paper has grown out from. We thank Vladyslav Zveryk for collaboration on Theorem 2.3 and on the corresponding Magma code which implements big algebras. We thank Hiraku Nakajima for discussions and pointing out Theorem 3.1.2, a result generalizing our original observation in the= = 0 case. Special thanks go to Leonid Rybnikov for patiently explaining his works, in particular crucial to Theorem 2.1. We thank Michel Brion, Michael Finkelberg, Oscar García-Prada, Jakub Löwit, Joel Kamnitzer, Friedrich Knop, Michael McBreen, Anton Mellit, Takuro Mochizuki, Shon Ngô, Kamil Rychlewicz, Shiyu Shen, Leslie Spencer, Balázs Szendr ˝ oi, András Szenes, and Oksana\r\nYakimova for comments and discussions. Kamil Rychlewicz and Daniel Bedats helped with the Mathematica files for the figures, and we used the SM_isospin Tikz package of Izaak Neutelings for drawing the baryon multiplets. We thank the referees for many useful comments. We acknowledge funding from FWF grant “Geometry of the tip of the global nilpotent cone” no. P 35847.","ddc":["510"],"date_updated":"2026-10-21T10:58:34Z","publisher":"National Academy of Sciences","_id":"18108","title":"Commutative avatars of representations of semisimple Lie groups","publication_identifier":{"eissn":["1091-6490"]},"abstract":[{"text":"Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are commutative finite flat algebras over the cohomology of the classifying space of the group. They are isomorphic with the equivariant intersection cohomology of affine Schubert varieties, endowing the latter with a new ring structure. Study of the finer aspects of the structure of the big algebras will also furnish the stalks of the intersection cohomology with ring structure, thus ringifying Lusztig’s q-weight multiplicity polynomials i.e., certain affine Kazhdan–Lusztig polynomials.","lang":"eng"}],"citation":{"apa":"Hausel, T. (2024). Commutative avatars of representations of semisimple Lie groups. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2319341121\">https://doi.org/10.1073/pnas.2319341121</a>","mla":"Hausel, Tamás. “Commutative Avatars of Representations of Semisimple Lie Groups.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 121, no. 38, e2319341121, National Academy of Sciences, 2024, doi:<a href=\"https://doi.org/10.1073/pnas.2319341121\">10.1073/pnas.2319341121</a>.","ista":"Hausel T. 2024. Commutative avatars of representations of semisimple Lie groups. Proceedings of the National Academy of Sciences of the United States of America. 121(38), e2319341121.","ieee":"T. Hausel, “Commutative avatars of representations of semisimple Lie groups,” <i>Proceedings of the National Academy of Sciences of the United States of America</i>, vol. 121, no. 38. National Academy of Sciences, 2024.","ama":"Hausel T. Commutative avatars of representations of semisimple Lie groups. <i>Proceedings of the National Academy of Sciences of the United States of America</i>. 2024;121(38). doi:<a href=\"https://doi.org/10.1073/pnas.2319341121\">10.1073/pnas.2319341121</a>","chicago":"Hausel, Tamás. “Commutative Avatars of Representations of Semisimple Lie Groups.” <i>Proceedings of the National Academy of Sciences of the United States of America</i>. National Academy of Sciences, 2024. <a href=\"https://doi.org/10.1073/pnas.2319341121\">https://doi.org/10.1073/pnas.2319341121</a>.","short":"T. Hausel, Proceedings of the National Academy of Sciences of the United States of America 121 (2024)."},"doi":"10.1073/pnas.2319341121","file_date_updated":"2024-09-23T11:22:56Z","article_processing_charge":"Yes (in subscription journal)","department":[{"_id":"TaHa"}],"has_accepted_license":"1","corr_author":"1","project":[{"_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone","grant_number":"P35847"}],"dataavailabilitystatement":"There are no data underlying this work.\r\n","article_number":"e2319341121","oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"month":"09","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","issue":"38","year":"2024","status":"public","researchdata_availability":"not applicable","intvolume":"       121","related_material":{"link":[{"url":"https://ista.ac.at/en/news/big-algebras-a-dictionary-of-abstract-math/","relation":"press_release"}]},"date_published":"2024-09-17T00:00:00Z","oa":1,"date_created":"2024-09-22T22:01:41Z","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication":"Proceedings of the National Academy of Sciences of the United States of America","fulldoi":"https://doi.org/10.1073/pnas.2319341121","publication_status":"published","file":[{"access_level":"open_access","date_created":"2024-09-23T11:22:56Z","file_name":"2024_PNAS_Hausel.pdf","checksum":"df80c873633c6734d2e324841e69db58","date_updated":"2024-09-23T11:22:56Z","relation":"main_file","content_type":"application/pdf","file_id":"18127","success":1,"file_size":3764695,"creator":"dernst"}],"quality_controlled":"1","pmid":1,"article_type":"original","OA_type":"hybrid","supplementarymaterial":"no","volume":121,"das_tickbox":"1","OA_place":"publisher","day":"17","author":[{"last_name":"Hausel","orcid":"0000-0002-9582-2634","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","first_name":"Tamás"}]},{"volume":35,"supplementarymaterial":"no","quality_controlled":"1","article_type":"original","day":"04","author":[{"last_name":"González","full_name":"González, Miguel","first_name":"Miguel"},{"full_name":"Hausel, Tamás","first_name":"Tamás","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9582-2634"}],"isi":1,"das_tickbox":"0","oa":1,"date_published":"2024-04-04T00:00:00Z","date_created":"2024-04-21T22:00:54Z","issue":"09","type":"journal_article","intvolume":"        35","status":"public","researchdata_availability":"no","year":"2024","publication":"International Journal of Mathematics","publication_status":"published","arxiv":1,"fulldoi":"https://doi.org/10.1142/S0129167X2441009X","article_number":"2441009","project":[{"name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","grant_number":"P35847"}],"scopus_import":"1","month":"04","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2303.01404"}],"title":"Hitchin map on even very stable upward flows","acknowledgement":"Most of the research for this paper was done when the first author visited the second author's group at IST Austria as a summer intern in 2022. The second author was supported by an FWF grant \"Geometry of the top of the nilpotent cone\" number P35847.","external_id":{"isi":["001251179200003"],"arxiv":["2303.01404"]},"_id":"15339","publisher":"World Scientific Publishing","date_updated":"2026-10-21T10:57:37Z","department":[{"_id":"TaHa"}],"citation":{"ieee":"M. González and T. Hausel, “Hitchin map on even very stable upward flows,” <i>International Journal of Mathematics</i>, vol. 35, no. 09. World Scientific Publishing, 2024.","ista":"González M, Hausel T. 2024. Hitchin map on even very stable upward flows. International Journal of Mathematics. 35(09), 2441009.","short":"M. González, T. Hausel, International Journal of Mathematics 35 (2024).","chicago":"González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward Flows.” <i>International Journal of Mathematics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/S0129167X2441009X\">https://doi.org/10.1142/S0129167X2441009X</a>.","ama":"González M, Hausel T. Hitchin map on even very stable upward flows. <i>International Journal of Mathematics</i>. 2024;35(09). doi:<a href=\"https://doi.org/10.1142/S0129167X2441009X\">10.1142/S0129167X2441009X</a>","mla":"González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward Flows.” <i>International Journal of Mathematics</i>, vol. 35, no. 09, 2441009, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/S0129167X2441009X\">10.1142/S0129167X2441009X</a>.","apa":"González, M., &#38; Hausel, T. (2024). Hitchin map on even very stable upward flows. <i>International Journal of Mathematics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129167X2441009X\">https://doi.org/10.1142/S0129167X2441009X</a>"},"doi":"10.1142/S0129167X2441009X","abstract":[{"text":"We define even very stable Higgs bundles and study the Hitchin map restricted to their upward flows. In the GLn case, we classify the type (1,…,1) examples, and find that they are governed by a root system formed by the roots of even height. We discuss how the spectrum of equivariant cohomology of real and quaternionic Grassmannians, 4n-spheres and the real Cayley plane appear to describe the Hitchin map on even cominuscule upward flows. The even upward flows in question are the same as upward flows in Higgs bundle moduli spaces for quasi-split inner real forms. The latter spaces have been pioneered by Oscar García-Prada and his collaborators.","lang":"eng"}],"publication_identifier":{"issn":["0129-167X"],"eissn":["1793-6519"]},"article_processing_charge":"No"}]