On Characters of Irreducible Highest Weight Modules of Negative Integer Level over Affine Lie Algebras

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 andCn (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.