正则元素的Lusztig变种

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-09-18 DOI:10.1016/j.jalgebra.2025.09.008

Xuhua He, Ruben La

{"title":"正则元素的Lusztig变种","authors":"Xuhua He, Ruben La","doi":"10.1016/j.jalgebra.2025.09.008","DOIUrl":null,"url":null,"abstract":"<div><div>Let <math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math> be a connected reductive group over an algebraically closed field. Let B be a Borel subgroup of <math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math> and W be the associated Weyl group. We show that for any <math><mi>w</mi><mo>∈</mo><mi>W</mi></math> that is not contained in any standard parabolic subgroup of W, the intersection of the Bruhat cell BwB with any regular conjugacy class of <math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math> is always irreducible. We then prove that the associated Lusztig varieties are irreducible. This extends the previous work of Kim [7] on the regular semisimple and regular unipotent elements. The irreducibility result of Lusztig varieties will be used in an upcoming work in the study of affine Lusztig varieties.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"686 ","pages":"Pages 845-853"},"PeriodicalIF":0.8000,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lusztig varieties for regular elements\",\"authors\":\"Xuhua He, Ruben La\",\"doi\":\"10.1016/j.jalgebra.2025.09.008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math> be a connected reductive group over an algebraically closed field. Let B be a Borel subgroup of <math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math> and W be the associated Weyl group. We show that for any <math><mi>w</mi><mo>∈</mo><mi>W</mi></math> that is not contained in any standard parabolic subgroup of W, the intersection of the Bruhat cell BwB with any regular conjugacy class of <math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math> is always irreducible. We then prove that the associated Lusztig varieties are irreducible. This extends the previous work of Kim [7] on the regular semisimple and regular unipotent elements. The irreducibility result of Lusztig varieties will be used in an upcoming work in the study of affine Lusztig varieties.</div></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":\"686 \",\"pages\":\"Pages 845-853\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869325005332\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869325005332","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设G0是代数闭域上的连通约化群。设B为G0的Borel子群，W为相关联的Weyl群。证明了对于不包含在w的任何标准抛物子群中的任意w∈w， Bruhat元BwB与任意正则共轭类G0的交总是不可约的。然后我们证明了相关的Lusztig变量是不可约的。这扩展了Kim[7]先前关于正则半单元和正则单元的工作。Lusztig品种的不可约性结果将在今后对仿射Lusztig品种的研究中得到应用。

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

Lusztig varieties for regular elements

Let

G_{0}

be a connected reductive group over an algebraically closed field. Let B be a Borel subgroup of

G_{0}

and W be the associated Weyl group. We show that for any

w \in W

that is not contained in any standard parabolic subgroup of W, the intersection of the Bruhat cell BwB with any regular conjugacy class of

G_{0}

is always irreducible. We then prove that the associated Lusztig varieties are irreducible. This extends the previous work of Kim [7] on the regular semisimple and regular unipotent elements. The irreducibility result of Lusztig varieties will be used in an upcoming work in the study of affine Lusztig varieties.

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 Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.