Koszul duality for Kac–Moody groups and characters of tilting modules

Abstract

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