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

Achar, Pramod; Makisumi, Shotaro; Riche, Simon; Williamson, Geordie

doi:10.1090/jams/905

Koszul duality for Kac–Moody groups and characters of tilting modules
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by Pramod N. Achar, Shotaro Makisumi, Simon Riche and Geordie Williamson

J. Amer. Math. Soc. 32 (2019), 261-310

DOI: https://doi.org/10.1090/jams/905

Published electronically: August 2, 2018

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Abstract:

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

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