Weyl modules associated to Kac-Moody Lie algebras

TL;DR

This paper extends the concept of Weyl modules from affine Lie algebras to general Kac-Moody algebras tensorized with finitely generated commutative algebras, and proves a tensor product decomposition theorem.

Contribution

It introduces a generalized definition of Weyl modules for Kac-Moody algebras and establishes a tensor product decomposition theorem for these modules.

Findings

Generalized Weyl modules for Kac-Moody algebras are defined.

Proved a tensor product decomposition theorem for these modules.

Extended previous results from affine to Kac-Moody Lie algebras.

Abstract

Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in \cite{CP}. In this paper we extend the notion of Weyl modules for a Lie algebra $\mathfrak{g} \otimes A$, where $\mathfrak{g}$ is any Kac-Moody algebra and A is any finitely generated commutative associative algebra with unit over $\mathbb{C}$, and prove a tensor product decomposition theorem generalizing \cite{CP}.