Weyl Modules for Toroidal Lie Algebras

IF 0.6 4区数学 Q3 MATHEMATICS Algebras and Representation Theory Pub Date : 2022-12-20 DOI:10.1007/s10468-022-10187-6

Sudipta Mukherjee, Santosha Kumar Pattanayak, Sachin S. Sharma

引用次数: 0

Abstract

In this paper, we study Weyl modules for a toroidal Lie algebra \(\mathcal {T}\) with arbitrary n variables. Using the work of Rao (Pac. J. Math. 171(2), 511–528 1995), we prove that the level one global Weyl modules of \(\mathcal {T}\) are isomorphic to suitable submodules of a Fock space representation of \(\mathcal {T}\) up to a twist. As an application, we compute the graded character of the level one local Weyl module of \(\mathcal {T}\), thereby generalising the work of Kodera (Lett. Math. Phys. 110(11) 3053–3080 2020).

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环面李代数的Weyl模

在本文中，我们研究了具有任意 n 个变量的环形李代数（\mathcal {T}\）的 Weyl 模块。利用拉奥（Pac.J. Math.171(2), 511-528 1995），我们证明了 \(\mathcal {T}\) 的一级全局韦尔模块是与\(\mathcal {T}\) 的 Fock 空间表示的合适子模块同构的，直到扭转为止。作为应用，我们计算了 \(\mathcal {T}\) 的一级局部韦尔模块的分级特征，从而推广了柯德拉的工作（Lett.Math.110(11) 3053-3080 2020）的工作。

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.

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