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.References
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Bibliographic 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
- MR Author ID: 956295
- 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). - © Copyright 2018 American Mathematical Society
- Journal: J. Amer. Math. Soc. 32 (2019), 261-310
- MSC (2010): Primary 20G05
- DOI: https://doi.org/10.1090/jams/905
- MathSciNet review: 3868004