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


Authors: Pramod N. Achar, Shotaro Makisumi, Simon Riche and Geordie Williamson
Journal: J. Amer. Math. Soc. 32 (2019), 261-310
MSC (2010): Primary 20G05
DOI: https://doi.org/10.1090/jams/905
Published electronically: August 2, 2018
MathSciNet review: 3868004
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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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Additional Information

Pramod N. Achar
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
MR Author ID: 701892
Email: pramod@math.lsu.edu

Shotaro Makisumi
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: makisumi@math.columbia.edu

Simon Riche
Affiliation: Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
MR Author ID: 834430
Email: simon.riche@uca.fr

Geordie Williamson
Affiliation: School of Mathematics and Statistics F07, University of Sydney NSW 2006, Australia
MR Author ID: 845262
Email: g.williamson@sydney.edu.au

Received by editor(s): June 21, 2017
Received by editor(s) in revised form: June 4, 2018
Published electronically: August 2, 2018
Additional Notes: The first author was supported by NSF Grant No. DMS-1500890.
The third author was partially supported by ANR Grant No. ANR-13-BS01-0001-01. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 677147).
Article copyright: © Copyright 2018 American Mathematical Society