Weyl modules for toroidal Lie algebras

Abstract

In this paper we study Weyl modules for a toroidal Lie algebra $\CT$ with arbitrary $n$ variables. Using the work of Rao \cite{1995}, 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 \cite{ko}.