[{"DOAJ_listed":"1","_id":"21718","year":"2026","article_type":"original","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.3842/SIGMA.2026.024","OA_type":"diamond","date_created":"2026-04-12T22:01:51Z","has_accepted_license":"1","publisher":"National Academy of Science of Ukraine","language":[{"iso":"eng"}],"publication":"Symmetry, Integrability and Geometry: Methods and Applications","date_updated":"2026-04-16T06:11:12Z","corr_author":"1","file":[{"checksum":"29b28b5f8717ed1a084a2b551d0fd284","file_name":"2026_SIGMA_Ngo.pdf","success":1,"access_level":"open_access","date_updated":"2026-04-16T06:06:54Z","relation":"main_file","content_type":"application/pdf","file_id":"21740","creator":"dernst","file_size":975460,"date_created":"2026-04-16T06:06:54Z"}],"file_date_updated":"2026-04-16T06:06:54Z","publication_status":"published","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."}],"article_number":"024","arxiv":1,"ddc":["510"],"quality_controlled":"1","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.","scopus_import":"1","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"OA_place":"publisher","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"},{"grant_number":"27483","_id":"e6c64f42-ab3c-11f0-94c7-a95658059ccc","name":"Big algebras in classical types"}],"external_id":{"arxiv":["2501.04605"]},"publication_identifier":{"eissn":["1815-0659"]},"title":"Big algebra in type A for the coordinate ring of the matrix space","intvolume":"        22","volume":22,"department":[{"_id":"TaHa"}],"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>.","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.","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>","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.","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>."},"author":[{"full_name":"Ngo, Nhok T","id":"28e53c8c-896a-11ed-bdf8-f809043ce2f0","first_name":"Nhok T","last_name":"Ngo"}],"type":"journal_article","month":"03","day":"14","oa_version":"Published Version","article_processing_charge":"No","date_published":"2026-03-14T00:00:00Z","status":"public"},{"doi":"10.1007/s00031-026-09958-y","OA_type":"hybrid","date_created":"2026-03-23T15:10:43Z","has_accepted_license":"1","oa":1,"das_tickbox":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2026","article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00031-026-09958-y"}],"_id":"21489","arxiv":1,"quality_controlled":"1","ddc":["510"],"abstract":[{"lang":"eng","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."}],"publication_status":"epub_ahead","corr_author":"1","date_updated":"2026-07-22T07:37:35Z","language":[{"iso":"eng"}],"publisher":"Springer Nature","publication":"Transformation Groups","title":"On involutions of minuscule Kirillov algebras induced by real structures","publication_identifier":{"issn":["1083-4362"],"eissn":["1531-586X"]},"OA_place":"publisher","external_id":{"arxiv":["2411.16270"]},"project":[{"grant_number":"P35847","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone"}],"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). ","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa_version":"Published Version","status":"public","date_published":"2026-03-14T00:00:00Z","article_processing_charge":"Yes (via OA deal)","day":"14","month":"03","citation":{"ieee":"M. M. Elkner, “On involutions of minuscule Kirillov algebras induced by real structures,” <i>Transformation Groups</i>. Springer Nature, 2026.","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>.","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>","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>","ista":"Elkner MM. 2026. On involutions of minuscule Kirillov algebras induced by real structures. Transformation Groups.","short":"M.M. Elkner, Transformation Groups (2026).","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>."},"department":[{"_id":"TaHa"}],"type":"journal_article","author":[{"full_name":"Elkner, Mischa M","first_name":"Mischa M","id":"477faa59-080d-11ed-979a-c693ab7638ab","last_name":"Elkner"}]},{"corr_author":"1","date_updated":"2026-08-18T07:13:09Z","language":[{"iso":"eng"}],"publisher":"EMS Press","publication":"Documenta Mathematica","arxiv":1,"quality_controlled":"1","ddc":["500"],"PlanS_conform":"1","publication_status":"epub_ahead","abstract":[{"lang":"eng","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."}],"year":"2026","article_type":"original","supplementarymaterial":"no","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"],"main_file_link":[{"url":"https://doi.org/10.4171/DM/1064","open_access":"1"}],"_id":"22693","OA_type":"hybrid","doi":"10.4171/dm/1064","date_created":"2026-08-12T13:29:17Z","has_accepted_license":"1","oa":1,"das_tickbox":"0","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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>.","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).","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>","ista":"Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica."},"department":[{"_id":"GradSch"},{"_id":"TaHa"}],"mathsc":["19E08","19L47","20G44","14G17","19D55","14F43","14L30","14D24","14M25"],"type":"journal_article","author":[{"full_name":"Löwit, Jakub","last_name":"Löwit","id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0","first_name":"Jakub"}],"oa_version":"Published Version","date_published":"2026-03-26T00:00:00Z","status":"public","article_processing_charge":"Yes (in subscription journal)","day":"26","related_material":{"record":[{"relation":"dissertation_contains","id":"22694","status":"for_moderation"}]},"month":"03","researchdata_availability":"no","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.","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"scopus_import":"1","title":"Equivariant K-theory, affine Grassmannian and perfection","publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"OA_place":"publisher","external_id":{"arxiv":["2409.18925"]},"project":[{"_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone","grant_number":"P35847"}]},{"article_type":"original","year":"2025","_id":"19071","DOAJ_listed":"1","has_accepted_license":"1","date_created":"2025-02-23T23:01:56Z","doi":"10.46298/epiga.2025.12591","OA_type":"gold","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"file":[{"date_updated":"2025-02-25T06:53:27Z","access_level":"open_access","success":1,"file_name":"2025_Epiga_Hausel.pdf","checksum":"3915c6f117461502f7103878460428df","file_size":3276395,"date_created":"2025-02-25T06:53:27Z","creator":"dernst","file_id":"19085","content_type":"application/pdf","relation":"main_file"}],"corr_author":"1","date_updated":"2025-04-15T06:31:58Z","publication":"Epijournal de Geometrie Algebrique","language":[{"iso":"eng"}],"publisher":"EPI Sciences","quality_controlled":"1","ddc":["510"],"arxiv":1,"article_number":"1","publication_status":"published","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2025-02-25T06:53:27Z","tmp":{"image":"/images/cc_by_sa.png","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","short":"CC BY-SA (4.0)"},"license":"https://creativecommons.org/licenses/by-sa/4.0/","scopus_import":"1","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”. ","intvolume":"         9","publication_identifier":{"eissn":["2491-6765"]},"title":"Spectrum of equivariant cohomology as a fixed point scheme","external_id":{"arxiv":["2212.11836"]},"project":[{"_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone","grant_number":"P35847"},{"grant_number":"26525","_id":"34cd0f74-11ca-11ed-8bc3-bf0492a14a24","name":"Topology of open smooth varieties with a torus action"}],"OA_place":"publisher","type":"journal_article","author":[{"last_name":"Hausel","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","orcid":"0000-0002-9582-2634"},{"id":"85A07246-A8BF-11E9-B4FA-D9E3E5697425","first_name":"Kamil P","last_name":"Rychlewicz","full_name":"Rychlewicz, Kamil P"}],"citation":{"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>.","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.","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).","ista":"Hausel T, Rychlewicz KP. 2025. Spectrum of equivariant cohomology as a fixed point scheme. Epijournal de Geometrie Algebrique. 9, 1.","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>"},"department":[{"_id":"TaHa"}],"volume":9,"date_published":"2025-02-03T00:00:00Z","status":"public","article_processing_charge":"Yes","oa_version":"Published Version","day":"03","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17157"}]},"month":"02"},{"_id":"19621","year":"2025","article_type":"original","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1090/ert/689","OA_type":"hybrid","has_accepted_license":"1","date_created":"2025-04-24T08:48:05Z","publisher":"American Mathematical Society","language":[{"iso":"eng"}],"publication":"Representation Theory","date_updated":"2025-05-05T06:59:07Z","corr_author":"1","file":[{"date_updated":"2025-05-05T06:57:49Z","file_name":"2025_RepresentationTheory_Nessonov.pdf","checksum":"f6541ea1736a7413c6d24f14d64a4dda","success":1,"access_level":"open_access","creator":"dernst","date_created":"2025-05-05T06:57:49Z","file_size":424364,"content_type":"application/pdf","file_id":"19644","relation":"main_file"}],"file_date_updated":"2025-05-05T06:57:49Z","publication_status":"published","abstract":[{"lang":"eng","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."}],"arxiv":1,"quality_controlled":"1","ddc":["510"],"issue":"8","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","scopus_import":"1","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)"},"OA_place":"publisher","page":"256-288","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"external_id":{"arxiv":["2206.01964"]},"publication_identifier":{"issn":["1088-4165"]},"title":"Indecomposable characters of inductive limits of symmetric groups","intvolume":"        29","volume":29,"department":[{"_id":"GradSch"},{"_id":"TaHa"}],"citation":{"ista":"Nessonov N, Ngo NT. 2025. Indecomposable characters of inductive limits of symmetric groups. Representation Theory. 29(8), 256–288.","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>","short":"N. Nessonov, N.T. Ngo, Representation Theory 29 (2025) 256–288.","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>.","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>.","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.","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>"},"author":[{"full_name":"Nessonov, Nikolay","last_name":"Nessonov","first_name":"Nikolay"},{"full_name":"Ngo, Nhok T","id":"28e53c8c-896a-11ed-bdf8-f809043ce2f0","first_name":"Nhok T","last_name":"Ngo"}],"type":"journal_article","month":"04","day":"10","oa_version":"Published Version","article_processing_charge":"Yes (in subscription journal)","status":"public","date_published":"2025-04-10T00:00:00Z"},{"date_published":"2024-04-04T00:00:00Z","status":"public","article_processing_charge":"No","oa_version":"Preprint","day":"04","month":"04","author":[{"last_name":"González","first_name":"Miguel","full_name":"González, Miguel"},{"full_name":"Hausel, Tamás","orcid":"0000-0002-9582-2634","last_name":"Hausel","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","citation":{"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>.","short":"M. González, T. Hausel, International Journal of Mathematics 35 (2024).","ista":"González M, Hausel T. 2024. Hitchin map on even very stable upward flows. International Journal of Mathematics. 35(09), 2441009.","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>","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>.","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."},"department":[{"_id":"TaHa"}],"volume":35,"intvolume":"        35","publication_identifier":{"eissn":["1793-6519"],"issn":["0129-167X"]},"title":"Hitchin map on even very stable upward flows","external_id":{"isi":["001251179200003"],"arxiv":["2303.01404"]},"project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"scopus_import":"1","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.","issue":"09","quality_controlled":"1","arxiv":1,"article_number":"2441009","publication_status":"published","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"}],"isi":1,"date_updated":"2025-09-04T13:40:37Z","publication":"International Journal of Mathematics","language":[{"iso":"eng"}],"publisher":"World Scientific Publishing","date_created":"2024-04-21T22:00:54Z","doi":"10.1142/S0129167X2441009X","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"article_type":"original","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2303.01404","open_access":"1"}],"year":"2024","_id":"15339"},{"publication_identifier":{"eissn":["1091-6490"]},"title":"Commutative avatars of representations of semisimple Lie groups","intvolume":"       121","OA_place":"publisher","external_id":{"pmid":["39259592"]},"project":[{"grant_number":"P35847","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone"}],"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.","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"scopus_import":"1","issue":"38","oa_version":"Published Version","date_published":"2024-09-17T00:00:00Z","status":"public","article_processing_charge":"Yes (in subscription journal)","day":"17","related_material":{"link":[{"url":"https://ista.ac.at/en/news/big-algebras-a-dictionary-of-abstract-math/","relation":"press_release"}]},"month":"09","citation":{"short":"T. Hausel, Proceedings of the National Academy of Sciences of the United States of America 121 (2024).","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>.","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>","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.","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>","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.","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>."},"department":[{"_id":"TaHa"}],"author":[{"last_name":"Hausel","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","orcid":"0000-0002-9582-2634"}],"type":"journal_article","volume":121,"OA_type":"hybrid","doi":"10.1073/pnas.2319341121","date_created":"2024-09-22T22:01:41Z","has_accepted_license":"1","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","APC_amount":"2742,92 EUR","pmid":1,"article_type":"original","_id":"18108","quality_controlled":"1","ddc":["510"],"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"}],"publication_status":"published","file_date_updated":"2024-09-23T11:22:56Z","article_number":"e2319341121","file":[{"relation":"main_file","file_id":"18127","content_type":"application/pdf","date_created":"2024-09-23T11:22:56Z","file_size":3764695,"creator":"dernst","access_level":"open_access","success":1,"checksum":"df80c873633c6734d2e324841e69db58","file_name":"2024_PNAS_Hausel.pdf","date_updated":"2024-09-23T11:22:56Z"}],"corr_author":"1","date_updated":"2025-05-08T09:57:59Z","language":[{"iso":"eng"}],"publisher":"National Academy of Sciences","publication":"Proceedings of the National Academy of Sciences of the United States of America"}]