{"title":"乔丹对应和字符块分布","authors":"Radha Kessar, Gunter Malle","doi":"10.1112/jlms.70076","DOIUrl":null,"url":null,"abstract":"<p>We complete the determination of the <span></span><math>\n <semantics>\n <mi>ℓ</mi>\n <annotation>$\\ell$</annotation>\n </semantics></math>-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the <span></span><math>\n <semantics>\n <mi>ℓ</mi>\n <annotation>$\\ell$</annotation>\n </semantics></math>-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from <span></span><math>\n <semantics>\n <mi>ℓ</mi>\n <annotation>$\\ell$</annotation>\n </semantics></math> has connected centre. As a consequence, we derive a compatibility between <span></span><math>\n <semantics>\n <mi>ℓ</mi>\n <annotation>$\\ell$</annotation>\n </semantics></math>-blocks, <span></span><math>\n <semantics>\n <mi>e</mi>\n <annotation>$e$</annotation>\n </semantics></math>-Harish-Chandra series and Jordan decomposition. Further, we apply our results to complete the proof of Robinson's conjecture on defects of characters.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70076","citationCount":"0","resultStr":"{\"title\":\"Jordan correspondence and block distribution of characters\",\"authors\":\"Radha Kessar, Gunter Malle\",\"doi\":\"10.1112/jlms.70076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We complete the determination of the <span></span><math>\\n <semantics>\\n <mi>ℓ</mi>\\n <annotation>$\\\\ell$</annotation>\\n </semantics></math>-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the <span></span><math>\\n <semantics>\\n <mi>ℓ</mi>\\n <annotation>$\\\\ell$</annotation>\\n </semantics></math>-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from <span></span><math>\\n <semantics>\\n <mi>ℓ</mi>\\n <annotation>$\\\\ell$</annotation>\\n </semantics></math> has connected centre. As a consequence, we derive a compatibility between <span></span><math>\\n <semantics>\\n <mi>ℓ</mi>\\n <annotation>$\\\\ell$</annotation>\\n </semantics></math>-blocks, <span></span><math>\\n <semantics>\\n <mi>e</mi>\\n <annotation>$e$</annotation>\\n </semantics></math>-Harish-Chandra series and Jordan decomposition. Further, we apply our results to complete the proof of Robinson's conjecture on defects of characters.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"111 2\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-02-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70076\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70076\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70076","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Jordan correspondence and block distribution of characters
We complete the determination of the -block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the -block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from has connected centre. As a consequence, we derive a compatibility between -blocks, -Harish-Chandra series and Jordan decomposition. Further, we apply our results to complete the proof of Robinson's conjecture on defects of characters.
期刊介绍:
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.