环面李代数的Weyl模

Pub Date : 2022-12-20 DOI:10.1007/s10468-022-10187-6

Sudipta Mukherjee, Santosha Kumar Pattanayak, Sachin S. Sharma

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引用次数: 0

摘要

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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Weyl Modules for Toroidal Lie Algebras

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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