Characters of integrable highest weight modules over a quantum group

TL;DR

This paper proves that the Weyl-Kac character formula applies to integrable highest weight modules over quantum groups associated with symmetrizable Kac-Moody Lie algebras, for generic values of the parameter q.

Contribution

It extends the validity of the Weyl-Kac character formula to a broad class of quantum groups at generic q, covering all symmetrizable Kac-Moody cases.

Findings

Weyl-Kac character formula holds for these modules

Validity is established for q not a root of unity

Results apply to all symmetrizable Kac-Moody Lie algebras

Abstract

We show that the Weyl-Kac type character formula holds for the integrable highest weight modules over the quantized enveloping algebra of any symmetrizable Kac-Moody Lie algebra, when the parameter $q$ is not a root of unity.