{"title":"仿射delign - lusztig变体的扭轨积分和不可约分量","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":"{\"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}","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}
Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties
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.
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