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

Victor G. Kac; Minoru Wakimoto

paper

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

arXiv:1706.08387

Abstract

We prove a character formula for the irreducible modules from the category $O$ over the simple affine vertex algebra of type $A_{n}$ and $C_{n}$ $(n \geq 2)$ of level $k = - 1$ . We also give a conjectured character formula for types $D_{4}$ , $E_{6}$ , $E_{7}$ , $E_{8}$ and levels $k = - 1, \dots, - b$ , where $b = 2, 3, 4, 6$ respectively.