{"publication_status":"epub_ahead","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","year":"2026","department":[{"_id":"TaHa"}],"publisher":"Springer Nature","date_created":"2026-03-23T15:10:43Z","title":"On involutions of minuscule Kirillov algebras induced by real structures","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."}],"oa":1,"doi":"10.1007/s00031-026-09958-y","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). ","arxiv":1,"citation":{"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>.","ista":"Elkner MM. 2026. On involutions of minuscule Kirillov algebras induced by real structures. Transformation Groups.","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>","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>","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>."},"ddc":["510"],"article_processing_charge":"Yes (via OA deal)","date_updated":"2026-03-24T08:26:10Z","day":"14","project":[{"grant_number":"P35847","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3","name":"Geometry of the tip of the global nilpotent cone"}],"main_file_link":[{"url":"https://doi.org/10.1007/s00031-026-09958-y","open_access":"1"}],"quality_controlled":"1","publication":"Transformation Groups","type":"journal_article","corr_author":"1","author":[{"first_name":"Mischa M","last_name":"Elkner","id":"477faa59-080d-11ed-979a-c693ab7638ab","full_name":"Elkner, Mischa M"}],"date_published":"2026-03-14T00:00:00Z","month":"03","language":[{"iso":"eng"}],"external_id":{"arxiv":["2411.16270"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","status":"public","publication_identifier":{"issn":["1083-4362"],"eissn":["1531-586X"]},"_id":"21489"}