Weyl modules for twisted toroidal Lie algebras

TL;DR

This paper extends the concept of Weyl modules to twisted toroidal Lie algebras, establishing their structure and calculating graded characters, thus advancing the understanding of their representation theory.

Contribution

It introduces Weyl modules for twisted toroidal Lie algebras and proves their isomorphism to tensor products involving twisted affine Lie algebra representations.

Findings

Level one global Weyl modules are isomorphic to tensor products of twisted affine Lie algebra modules and lattice vertex algebras.

Calculated the graded character of level one local Weyl modules.

Enhanced understanding of the structure and representation theory of twisted toroidal Lie algebras.

Abstract

In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra $\mathcal{T}(\mu)$. We prove that the level one global Weyl modules of $\mathcal{T}(\mu)$ are isomorphic to the tensor product of the level one representation of twisted affine Lie algebras and certain lattice vertex algebras. As a byproduct, we calculate the graded character of the level one local Weyl modules of $\mathcal{T}(\mu)$.