The Deformed Tanisaki-Garsia-Procesi Modules

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-09-20 DOI:10.1007/s10468-024-10288-4

Maico Freitas, Evgeny Mukhin

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 \(\mathfrak {sl}_{n+1}[t^{\pm 1}]\).

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变形Tanisaki-Garsia-Procesi模块

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

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.