虚拟莫里塔等价和布劳尔特征双射

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-05-29 DOI:10.1007/s00013-024-02010-z

Xin Huang

{"title":"虚拟莫里塔等价和布劳尔特征双射","authors":"Xin Huang","doi":"10.1007/s00013-024-02010-z","DOIUrl":null,"url":null,"abstract":"<div>We extend a theorem of Kessar and Linckelmann concerning Morita equivalences and Galois compatible bijections between Brauer characters to virtual Morita equivalences. As a corollary, we obtain that the block version of Navarro’s refinement of Alperin’s weight conjecture holds for blocks with cyclic and Klein four defect groups, blocks of symmetric and alternating groups with abelian defect groups, and p-Blocks of \\(\\textrm{SL}_2(q)\\) and \\(\\textrm{GL}_2(q)\\), where p|q.</div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Virtual Morita equivalences and Brauer character bijections\",\"authors\":\"Xin Huang\",\"doi\":\"10.1007/s00013-024-02010-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We extend a theorem of Kessar and Linckelmann concerning Morita equivalences and Galois compatible bijections between Brauer characters to virtual Morita equivalences. As a corollary, we obtain that the block version of Navarro’s refinement of Alperin’s weight conjecture holds for blocks with cyclic and Klein four defect groups, blocks of symmetric and alternating groups with abelian defect groups, and p-Blocks of \\\\(\\\\textrm{SL}_2(q)\\\\) and \\\\(\\\\textrm{GL}_2(q)\\\\), where p|q.</div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-02010-z\",\"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/s00013-024-02010-z","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

摘要

我们将 Kessar 和 Linckelmann 关于布劳尔字符之间的莫里塔等价性和伽罗瓦相容双射的定理扩展到虚拟莫里塔等价性。作为推论，我们得到纳瓦罗对阿尔佩林权重猜想的区块版本的完善，对于具有循环群和克莱因四缺陷群的区块、具有非等缺陷群的对称群和交替群的区块，以及 p|q 的 \(\textrm{SL}_2(q)\) 和 \(\textrm{GL}_2(q)\) 的 p 区块都成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Virtual Morita equivalences and Brauer character bijections

We extend a theorem of Kessar and Linckelmann concerning Morita equivalences and Galois compatible bijections between Brauer characters to virtual Morita equivalences. As a corollary, we obtain that the block version of Navarro’s refinement of Alperin’s weight conjecture holds for blocks with cyclic and Klein four defect groups, blocks of symmetric and alternating groups with abelian defect groups, and p-Blocks of \(\textrm{SL}_2(q)\) and \(\textrm{GL}_2(q)\), where p|q.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

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.