Weyl modules for toroidal Lie algebras

2022/03/03 by Sudipta Mukherjee, Mukherjee, Sudipta, Santosha Pattanayak +3 · 1 citation
Mathematics · #17B67 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2203.01715

openalex publication_date 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study Weyl modules for a toroidal Lie algebra \CT with arbitrary n variables. Using the work of Rao \cite1995, we prove that the level one global Weyl modules of \CT are isomorphic to suitable submodules of a Fock space representation of \CT upto a twist. As an application, we compute the graded character of the level one local Weyl module of \CT, thereby generalising the work of Kodera \citeko.

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