# Character Formulas from Matrix Factorizations

## TL;DR

This paper introduces a unified approach using matrix factorizations and Chern character constructions to derive character formulas for Lie group representations, simplifying and generalizing previous methods.

## Contribution

It presents a novel, unified method based on matrix factorizations and highest-weight theory to prove character formulas for various Lie groups, including compact and semisimple cases.

## Key findings

- Recover the Kirillov formula for compact groups
- Derive Rossman character formula for real semisimple groups
- Method relies mainly on highest-weight theory

## Abstract

In this paper I present a new and unified method of proving character formulas for discrete series representations of connected Lie groups by applying a Chern character-type construction to the matrix factorizations of [FT] and [FHT3]. In the case of a compact group I recover the Kirillov formula, thereby exhibiting the work of [FT] as a categorification of the Kirillov correspondence. In the case of a real semisimple group I recover the Rossman character formula with only a minimal amount of analysis. The appeal of this method is that it relies almost entirely on highest-weight theory, which is a far more ubiquitous phenomenon than the varied techniques that were previously used to prove such formulas.