{"title":"Localized calculus for the Hecke category","authors":"Ben Elias, Geordie Williamson","doi":"10.5802/ambp.415","DOIUrl":null,"url":null,"abstract":"We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules.","PeriodicalId":52347,"journal":{"name":"Annales Mathematiques Blaise Pascal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematiques Blaise Pascal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/ambp.415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 10
Abstract
We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules.
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