A Note on Schur-Weyl Dualities for GL(m) and GL(m|n)

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-09-17 DOI:10.1007/s10468-024-10290-w

František Marko

引用次数: 0

Abstract

We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities describe the endomorphism algebras of the tensor space and mixed tensor space, respectively, over the group algebra of the symmetric group and the Brauer wall algebra, respectively. Our main new results are the second part of the mixed Schur-Weyl dualities and mixed super Schur-Weyl dualities over an infinite ground field of positive characteristic.

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关于 GL(m) 和 GL(m|n) 的舒尔-韦尔对偶性的说明

我们用统一的基本方法证明了任意特征无限地域上一般线性群和超群的经典、混合、超和混合超舒尔韦耳对偶性的第二部分。这些对偶性分别描述了对称群的群代数和布劳尔壁代数上的张量空间和混合张量空间的内象代数。我们的主要新成果是正特征无限地域上的混合舒尔-韦尔对偶性和混合超舒尔-韦尔对偶性的第二部分。

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.