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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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 HTML | PDF
J. Amer. Math. Soc. 32 (2019), 261-310 Request permission

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
  • 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