# Koszul duality for Kac-Moody groups and characters of tilting modules

## TL;DR

This paper develops a character formula for tilting modules in reductive groups over fields of characteristic p, extending Koszul duality to modular coefficients and linking it to p-Kazhdan-Lusztig polynomials.

## Contribution

It extends monoidal Koszul duality to modular coefficients and provides new character formulas for tilting and simple modules in positive characteristic.

## Key findings

- Character formula for indecomposable tilting modules in terms of p-Kazhdan-Lusztig polynomials
- Extension of Koszul duality to modular coefficients
- Deduction of simple module character formulas for p>2h-3

## Abstract

We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxeter number. Using results of Andersen, one may deduce a character formula for simple modules if p>2h-3. Our results are a consequence of an extension to modular coefficients of a monoidal Koszul duality equivalence established by Bezrukavnikov and Yun.