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

Pramod N Achar (1) , Shotaro Makisumi (2) , Simon Riche (3, 4) , Geordie Williamson (5)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 Department of Mathematics [Stanford]
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
5 The University of Sydney

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−2. Our results are a consequence of an extension to modular coefficients of a monoidal Koszul duality equivalence established by Bezrukavnikov and Yun.

Domaines: Mathématiques [math]

Pramod N Achar, Shotaro Makisumi, Simon Riche, Geordie Williamson. Koszul duality for Kac-Moody groups and characters of tilting modules. Journal of the American Mathematical Society, 2019, 32 (1), pp.261-310. ⟨hal-01531873⟩