[{"date_updated":"2026-07-22T07:37:35Z","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"}],"_id":"21489","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00031-026-09958-y"}],"citation":{"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>","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>","short":"M.M. Elkner, Transformation Groups (2026).","ieee":"M. M. Elkner, “On involutions of minuscule Kirillov algebras induced by real structures,” <i>Transformation Groups</i>. Springer Nature, 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>.","ista":"Elkner MM. 2026. On involutions of minuscule Kirillov algebras induced by real structures. Transformation Groups.","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>."},"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00031-026-09958-y","article_type":"original","external_id":{"arxiv":["2411.16270"]},"date_created":"2026-03-23T15:10:43Z","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). ","publication":"Transformation Groups","license":"https://creativecommons.org/licenses/by/4.0/","publisher":"Springer Nature","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"date_published":"2026-03-14T00:00:00Z","day":"14","publication_identifier":{"eissn":["1531-586X"],"issn":["1083-4362"]},"OA_type":"hybrid","type":"journal_article","year":"2026","department":[{"_id":"TaHa"}],"month":"03","das_tickbox":"1","author":[{"full_name":"Elkner, Mischa M","first_name":"Mischa M","id":"477faa59-080d-11ed-979a-c693ab7638ab","last_name":"Elkner"}],"has_accepted_license":"1","status":"public","ddc":["510"],"OA_place":"publisher","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"quality_controlled":"1","publication_status":"epub_ahead","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"corr_author":"1","title":"On involutions of minuscule Kirillov algebras induced by real structures","oa_version":"Published Version"},{"doi":"10.1007/s00031-024-09873-0","dataavailabilitystatement":"Not applicable.","article_type":"original","acknowledgement":"I would like to warmly thank Dimitri Wyss for his guidance and supervision and Nero Budur for helpful discussions and answering all my questions on his previous works. I would also like to thank Francesca Carocci, Ben Davison, Lucien Hennecart and Olivier Schiffmann for helpful remarks and discussions during the writing of this paper. Finally, I would like to thank the anonymous referees for their careful reading and suggesting improvements in the exposition.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This work was supported by the Swiss National Science Foundation [No. 196960]. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","external_id":{"isi":["001287455300001"]},"date_created":"2024-08-18T22:01:04Z","ec_funded":1,"_id":"17437","citation":{"apa":"Vernet, T. (2026). Rational singularities for moment maps of totally negative quivers. <i>Transformation Groups</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00031-024-09873-0\">https://doi.org/10.1007/s00031-024-09873-0</a>","chicago":"Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative Quivers.” <i>Transformation Groups</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00031-024-09873-0\">https://doi.org/10.1007/s00031-024-09873-0</a>.","ama":"Vernet T. Rational singularities for moment maps of totally negative quivers. <i>Transformation Groups</i>. 2026;31:1047-1083. doi:<a href=\"https://doi.org/10.1007/s00031-024-09873-0\">10.1007/s00031-024-09873-0</a>","short":"T. Vernet, Transformation Groups 31 (2026) 1047–1083.","ieee":"T. Vernet, “Rational singularities for moment maps of totally negative quivers,” <i>Transformation Groups</i>, vol. 31. Springer Nature, pp. 1047–1083, 2026.","ista":"Vernet T. 2026. Rational singularities for moment maps of totally negative quivers. Transformation Groups. 31, 1047–1083.","mla":"Vernet, Tanguy. “Rational Singularities for Moment Maps of Totally Negative Quivers.” <i>Transformation Groups</i>, vol. 31, Springer Nature, 2026, pp. 1047–83, doi:<a href=\"https://doi.org/10.1007/s00031-024-09873-0\">10.1007/s00031-024-09873-0</a>."},"article_processing_charge":"Yes (via OA deal)","researchdata_availability":"not applicable","abstract":[{"lang":"eng","text":"We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were introduced by Budur. We also transfer the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau categories, based on recent work of Davison. This has interesting arithmetic applications on quiver moment maps and moduli spaces of objects in 2-Calabi-Yau categories. First, we generalize results of Wyss on the asymptotic behaviour of counts of jets of quiver moment maps over finite fields. Moreover, we interpret the limit of counts of jets on a given moduli space as its p-adic volume under a canonical measure analogous to the measure built by Carocci, Orecchia and Wyss on certain moduli spaces of coherent sheaves."}],"scopus_import":"1","date_updated":"2026-07-23T05:51:07Z","year":"2026","month":"03","department":[{"_id":"TaHa"}],"publication_identifier":{"eissn":["1531-586X"],"issn":["1083-4362"]},"OA_type":"hybrid","type":"journal_article","day":"01","publication":"Transformation Groups","publisher":"Springer Nature","file":[{"access_level":"open_access","checksum":"8985b4154b730284d3412ddc9e55d965","success":1,"content_type":"application/pdf","date_created":"2026-07-23T05:50:09Z","file_id":"22385","relation":"main_file","creator":"dernst","file_size":912029,"date_updated":"2026-07-23T05:50:09Z","file_name":"2026_TransformationGroups_Vernet.pdf"}],"date_published":"2026-03-01T00:00:00Z","project":[{"grant_number":"101034413","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"oa":1,"status":"public","ddc":["510"],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"OA_place":"publisher","isi":1,"supplementarymaterial":"no","intvolume":"        31","has_accepted_license":"1","das_tickbox":"1","author":[{"first_name":"Tanguy","full_name":"Vernet, Tanguy","last_name":"Vernet","id":"19f1e3bf-c59a-11ee-a1af-ed269948817b"}],"volume":31,"oa_version":"Published Version","PlanS_conform":"1","page":"1047-1083","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","title":"Rational singularities for moment maps of totally negative quivers","publication_status":"published","file_date_updated":"2026-07-23T05:50:09Z","mathsc":["14B05","14D23","14G20","16G20"],"quality_controlled":"1"},{"project":[{"grant_number":"320593","call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425","name":"Arithmetic and physics of Higgs moduli spaces"}],"date_published":"2020-12-01T00:00:00Z","publisher":"Springer Nature","publication":"Transformation Groups","day":"01","type":"journal_article","publication_identifier":{"issn":["1083-4362"],"eissn":["1531-586X"]},"month":"12","department":[{"_id":"TaHa"}],"year":"2020","date_updated":"2025-07-10T11:54:50Z","scopus_import":"1","abstract":[{"text":"We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18].","lang":"eng"}],"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.04375"}],"citation":{"ista":"Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation Groups. 25, 1371–1385.","mla":"Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation Groups</i>, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:<a href=\"https://doi.org/10.1007/s00031-020-09572-6\">10.1007/s00031-020-09572-6</a>.","short":"Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.","chicago":"Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” <i>Transformation Groups</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00031-020-09572-6\">https://doi.org/10.1007/s00031-020-09572-6</a>.","ama":"Yang Y, Zhao G. The PBW theorem for affine Yangians. <i>Transformation Groups</i>. 2020;25:1371-1385. doi:<a href=\"https://doi.org/10.1007/s00031-020-09572-6\">10.1007/s00031-020-09572-6</a>","ieee":"Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” <i>Transformation Groups</i>, vol. 25. Springer Nature, pp. 1371–1385, 2020.","apa":"Yang, Y., &#38; Zhao, G. (2020). The PBW theorem for affine Yangians. <i>Transformation Groups</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00031-020-09572-6\">https://doi.org/10.1007/s00031-020-09572-6</a>"},"_id":"7940","ec_funded":1,"acknowledgement":"Gufang Zhao is affiliated to IST Austria, Hausel group until July of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli spaces No. 320593 of the European Research Council.","external_id":{"arxiv":["1804.04375"],"isi":["000534874300003"]},"date_created":"2020-06-07T22:00:55Z","article_type":"original","doi":"10.1007/s00031-020-09572-6","quality_controlled":"1","publication_status":"published","title":"The PBW theorem for affine Yangians","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"page":"1371-1385","oa_version":"Preprint","volume":25,"author":[{"full_name":"Yang, Yaping","first_name":"Yaping","id":"360D8648-F248-11E8-B48F-1D18A9856A87","last_name":"Yang"},{"full_name":"Zhao, Gufang","first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao"}],"intvolume":"        25","isi":1,"status":"public","oa":1}]