{"title":"The Deformed Tanisaki-Garsia-Procesi Modules","authors":"Maico Freitas, Evgeny Mukhin","doi":"10.1007/s10468-024-10288-4","DOIUrl":null,"url":null,"abstract":"<div><p>The polynomial ideals studied by A. Garsia and C. Procesi play an important role in the theory of Kostka polynomials. We give multiparameter flat deformations of these ideals and define an action of the extended affine symmetric group on the corresponding quotient algebras multiplied by the sign representation. We show that the images of these modules under the affine Schur-Weyl duality are dual to the local Weyl modules for the loop algebra <span>\\(\\mathfrak {sl}_{n+1}[t^{\\pm 1}]\\)</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 6","pages":"2019 - 2044"},"PeriodicalIF":0.5000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10288-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The polynomial ideals studied by A. Garsia and C. Procesi play an important role in the theory of Kostka polynomials. We give multiparameter flat deformations of these ideals and define an action of the extended affine symmetric group on the corresponding quotient algebras multiplied by the sign representation. We show that the images of these modules under the affine Schur-Weyl duality are dual to the local Weyl modules for the loop algebra \(\mathfrak {sl}_{n+1}[t^{\pm 1}]\).
A. Garsia和C. Procesi研究的多项式理想在Kostka多项式理论中占有重要地位。我们给出了这些理想的多参数平面变形，并定义了扩展仿射对称群对相应商代数乘以符号表示的作用。我们证明了这些模在仿射Schur-Weyl对偶下的像对循环代数\(\mathfrak {sl}_{n+1}[t^{\pm 1}]\)的局部Weyl模是对偶的。
期刊介绍：
Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.
The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
