On characters of irreducible highest weight modules of negative integer level over affine lie algebras

Abstract

We prove a character formula for irreducible highest weight modules over a simple affine vertex algebra of level k, attached to a simple Lie algebra g, which are locally g-finite, in the cases when g is of type An and Cn (n≥2) and k = −1. We also conjecture a character formula for types D4, E6, E7, E8 and levels k = −1,.., −b, where b = 2, 3, 4, 6 respectively.