{"title":"扩展单能字符的合理性","authors":"Olivier Dudas, Gunter Malle","doi":"10.1007/s00013-024-02045-2","DOIUrl":null,"url":null,"abstract":"<div><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></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 5","pages":"455 - 466"},"PeriodicalIF":0.5000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02045-2.pdf","citationCount":"0","resultStr":"{\"title\":\"Rationality of extended unipotent characters\",\"authors\":\"Olivier Dudas, Gunter Malle\",\"doi\":\"10.1007/s00013-024-02045-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><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></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":\"123 5\",\"pages\":\"455 - 466\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00013-024-02045-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/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}
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.
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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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