Unique Factorization for Tensor Products of Parabolic Verma Modules

IF 0.5 4区数学 Q3 MATHEMATICS Algebras and Representation Theory Pub Date : 2024-02-01 DOI:10.1007/s10468-024-10254-0

K. N. Raghavan, V. Sathish Kumar, R. Venkatesh, Sankaran Viswanath

引用次数: 0

Abstract

Let \(\mathfrak g\) be a symmetrizable Kac-Moody Lie algebra with Cartan subalgebra \(\mathfrak h\). We prove a unique factorization property for tensor products of parabolic Verma modules. More generally, we prove unique factorization for products of characters of parabolic Verma modules when restricted to certain subalgebras of \(\mathfrak h\). These include fixed point subalgebras of \(\mathfrak h\) under subgroups of diagram automorphisms of \(\mathfrak g\) and twisted graph automorphisms in the affine case.

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抛物线维尔马模块张量乘的唯一因式分解

让 \(\mathfrak g\) 是一个具有 Cartan 子代数 \(\mathfrak h\) 的可对称 Kac-Moody Lie 代数。我们证明了抛物面 Verma 模块张量乘的唯一因式分解性质。更广义地说，我们证明了抛物面 Verma 模块的张量积的唯一因式分解性质，当它局限于 \(\mathfrak h\) 的某些子代数时。这些子代数包括在 \(\mathfrak g\) 的图自形子群下的\(\mathfrak h\) 的定点子代数，以及在仿射情况下的扭曲图自形子群下的\(\mathfrak g\) 的定点子代数。

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.