Wille Liu, Cheng-Chiang Tsai, Kari Vilonen, Ting Xue
{"title":"Cuspidal character sheaves on graded Lie algebras","authors":"Wille Liu, Cheng-Chiang Tsai, Kari Vilonen, Ting Xue","doi":"arxiv-2409.04030","DOIUrl":null,"url":null,"abstract":"We show in this paper that in the context of graded Lie algebras, all\ncuspidal character sheaves arise from a nearby-cycle construction followed by a\nFourier--Sato transform in a very specific manner. Combined with results of the\nlast two named authors, this completes the explicit description of cuspidal\ncharacter sheaves for Vinberg's type I graded classical Lie algebras.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show in this paper that in the context of graded Lie algebras, all
cuspidal character sheaves arise from a nearby-cycle construction followed by a
Fourier--Sato transform in a very specific manner. Combined with results of the
last two named authors, this completes the explicit description of cuspidal
character sheaves for Vinberg's type I graded classical Lie algebras.
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