{"title":"Rationality of extended unipotent characters","authors":"Olivier Dudas, Gunter Malle","doi":"10.1007/s00013-024-02045-2","DOIUrl":null,"url":null,"abstract":"<p>We determine the rationality properties of unipotent characters of finite reductive groups arising as fixed points of disconnected reductive groups under a Frobenius map. In the proof, we use realisations of characters in <span>\\(\\ell \\)</span>-adic cohomology groups of Deligne–Lusztig varieties as well as block theoretic considerations.</p>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00013-024-02045-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We determine the rationality properties of unipotent characters of finite reductive groups arising as fixed points of disconnected reductive groups under a Frobenius map. In the proof, we use realisations of characters in \(\ell \)-adic cohomology groups of Deligne–Lusztig varieties as well as block theoretic considerations.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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