Coxeter 型深层次 Deligne-Lusztig 方案的正交关系

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2024-05-22 DOI:10.1017/fms.2024.55

Olivier Dudas, Alexander B. Ivanov

{"title":"Coxeter 型深层次 Deligne-Lusztig 方案的正交关系","authors":"Olivier Dudas, Alexander B. Ivanov","doi":"10.1017/fms.2024.55","DOIUrl":null,"url":null,"abstract":"In this paper, we prove some orthogonality relations for representations arising from deep level Deligne–Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig [Lus04], and of Chan and the second author [CI21b]. Applications include the study of smooth representations of p-adic groups in the cohomology of p-adic Deligne–Lusztig spaces and their relation to the local Langlands correspondences. Also, the geometry of deep level Deligne–Lusztig schemes gets accessible, in the spirit of Lusztig’s work [Lus76].","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orthogonality relations for deep level Deligne–Lusztig schemes of Coxeter type\",\"authors\":\"Olivier Dudas, Alexander B. Ivanov\",\"doi\":\"10.1017/fms.2024.55\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove some orthogonality relations for representations arising from deep level Deligne–Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig [Lus04], and of Chan and the second author [CI21b]. Applications include the study of smooth representations of p-adic groups in the cohomology of p-adic Deligne–Lusztig spaces and their relation to the local Langlands correspondences. Also, the geometry of deep level Deligne–Lusztig schemes gets accessible, in the spirit of Lusztig’s work [Lus76].\",\"PeriodicalId\":56000,\"journal\":{\"name\":\"Forum of Mathematics Sigma\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum of Mathematics Sigma\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/fms.2024.55\",\"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":"Forum of Mathematics Sigma","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/fms.2024.55","RegionNum":2,"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

在本文中，我们证明了由 Coxeter 类型的深层 Deligne-Lusztig 方案产生的表示的一些正交关系。这概括了 Lusztig [Lus04]、Chan 和第二作者 [CI21b] 以前的结果。其应用包括研究 p-adic Deligne-Lusztig 空间同调中 p-adic 群的光滑表示及其与局部朗兰兹对应关系。此外，本着 Lusztig 工作[Lus76]的精神，深层 Deligne-Lusztig 方案的几何也变得容易理解了。

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

Orthogonality relations for deep level Deligne–Lusztig schemes of Coxeter type

In this paper, we prove some orthogonality relations for representations arising from deep level Deligne–Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig [Lus04], and of Chan and the second author [CI21b]. Applications include the study of smooth representations of p-adic groups in the cohomology of p-adic Deligne–Lusztig spaces and their relation to the local Langlands correspondences. Also, the geometry of deep level Deligne–Lusztig schemes gets accessible, in the spirit of Lusztig’s work [Lus76].

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

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.