Characters of highest weight modules over affine Lie algebras are meromorphic functions

TL;DR

This paper proves that characters of highest weight modules over affine Lie algebras are meromorphic functions with simple poles at zeros of real roots, providing insights into their singularities.

Contribution

It establishes the meromorphic nature of these characters and describes their singularities, extending understanding of affine Lie algebra representations.

Findings

Characters are meromorphic functions in the positive half of the Cartan subalgebra.

Singularities are at most simple poles at zeros of real roots.

Provides information about the nature of these singularities.

Abstract

We show that the characters of all highest weight modules over an affine Lie algebra with the highest weight away from the critical hyperplane are meromorphic functions in the positive half of Cartan subalgebra, their singularities being at most simple poles at zeros of real roots. We obtain some information about these singularities.