{"title":"Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties","authors":"Rong Zhou, Yihang Zhu","doi":"10.4310/CJM.2020.v8.n1.a3","DOIUrl":null,"url":null,"abstract":"We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition functions. As an application we prove a conjecture of Miaofen Chen and Xinwen Zhu, relating the set of irreducible components of an affine Deligne-Lusztig variety modulo the action of the $\\sigma$-centralizer group to the Mirkovic-Vilonen basis of a certain weight space of a representation of the Langlands dual group.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cambridge Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/CJM.2020.v8.n1.a3","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: 20
Abstract
We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition functions. As an application we prove a conjecture of Miaofen Chen and Xinwen Zhu, relating the set of irreducible components of an affine Deligne-Lusztig variety modulo the action of the $\sigma$-centralizer group to the Mirkovic-Vilonen basis of a certain weight space of a representation of the Langlands dual group.