Characters of representations of affine Kac-Moody Lie algebras at the critical level

TL;DR

This paper provides an explicit character formula for certain irreducible highest weight representations of affine Kac-Moody Lie algebras at the critical level, focusing on those integrable over the associated finite-dimensional Lie algebra.

Contribution

It introduces a new explicit character formula for irreducible highest weight modules at the critical level of affine Kac-Moody Lie algebras.

Findings

Explicit character formula derived for critical level representations

Applicable to integrable modules over finite-dimensional Lie algebra

Enhances understanding of representation theory at critical level

Abstract

We present an explicit character formula for the irreducible highest weight representations of the non-twisted affine Kac-Moody Lie algebra at the critical level which are integrable over the corresponding finite-dimensional simple Lie algebra.