{"title":"Seshadri stratifications and Schubert varieties: a geometric construction of a standard monomial theory","authors":"Rocco Chirivì, Xin Fang, Peter Littelmann","doi":"10.4310/pamq.2024.v20.n1.a5","DOIUrl":null,"url":null,"abstract":"A standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifications of Schubert varieties by their Schubert subvarieties and (2) the combinatorial LS‑path character formula for Demazure modules. The general theory of Seshadri stratifications is improved by using arbitrary linearization of the partial order and by weakening the definition of balanced stratification.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2024.v20.n1.a5","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
A standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifications of Schubert varieties by their Schubert subvarieties and (2) the combinatorial LS‑path character formula for Demazure modules. The general theory of Seshadri stratifications is improved by using arbitrary linearization of the partial order and by weakening the definition of balanced stratification.