伪约化群的不可约模

IF 2.5 1区数学 Q1 MATHEMATICS

Journal of the European Mathematical Society Pub Date : 2021-11-09 DOI:10.4171/jems/1153

Michael Bate, David I. Stewart

{"title":"伪约化群的不可约模","authors":"Michael Bate, David I. Stewart","doi":"10.4171/jems/1153","DOIUrl":null,"url":null,"abstract":"We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Irreducible modules for pseudo-reductive groups\",\"authors\":\"Michael Bate, David I. Stewart\",\"doi\":\"10.4171/jems/1153\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.\",\"PeriodicalId\":50003,\"journal\":{\"name\":\"Journal of the European Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2021-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the European Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jems/1153\",\"RegionNum\":1,\"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 European Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1153","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们通过处理伪约化群的情况，对域上光滑、连通仿射代数群的不可约表示进行了分类。我们将伪分裂伪约群的维数计算问题简化为分裂约情形和伪分裂伪约交换情形。此外，我们给出了后者的第一个结果，包括对排名第一的情况的相当完整的描述。

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

Irreducible modules for pseudo-reductive groups

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the split reductive case and the pseudo-split pseudo-reductive commutative case. Moreover, we give the first results on the latter, including a rather complete description of the rank one case.

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

Journal of the European Mathematical Society 数学-数学

CiteScore

4.50

自引率

0.00%

发文量

103

审稿时长

6-12 weeks

期刊介绍： The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS. The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards. Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004. The Journal of the European Mathematical Society is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.