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

## TL;DR

This paper derives character formulas for certain irreducible modules over affine Lie algebras at negative level, expanding understanding of their structure in representation theory.

## Contribution

It provides a proven character formula for modules over affine vertex algebras of types A and C at level -1, and conjectures for other types and levels.

## Key findings

- Proved character formula for type A and C at level -1
- Conjectured formulas for types D and E at various negative levels
- Enhanced understanding of module characters at negative levels

## Abstract

We prove a character formula for the irreducible modules from the category $\mathcal{O}$ 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 $k=-1, \cdots, -b$, where $b=2,3,4,6$ respectively.