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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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Coxeter orbits and Brauer trees III
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by Olivier Dudas and Raphaël Rouquier PDF
J. Amer. Math. Soc. 27 (2014), 1117-1145 Request permission

Abstract:

This article is the final one of a series of articles on certain blocks of modular representations of finite groups of Lie type and the associated geometry. We prove the conjecture of Broué on derived equivalences induced by the complex of cohomology of Deligne-Lusztig varieties in the case of Coxeter elements. We also prove a conjecture of Hiß, Lübeck, and Malle on the Brauer trees of the corresponding blocks. As a consequence, we determine the Brauer tree (in particular, the decomposition matrix) of the principal $\ell$-block of $E_7(q)$ when $\ell \mid \Phi _{18}(q)$ and $E_8(q)$ when $\ell \mid \Phi _{18}(q)$ or $\ell \mid \Phi _{30}(q)$.
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Additional Information
  • Olivier Dudas
  • Affiliation: Université Denis Diderot – Paris 7, UFR de Mathématiques, Institut de Mathématiques de Jussieu, Case 7012, 75205 Paris Cedex 13, France
  • MR Author ID: 883805
  • Email: dudas@math.jussieu.fr
  • Raphaël Rouquier
  • Affiliation: Department of Mathematics, UCLA, Box 951555, Los Angeles, California 90095-1555
  • MR Author ID: 353858
  • Email: rouquier@math.ucla.edu
  • Received by editor(s): October 16, 2012
  • Received by editor(s) in revised form: August 16, 2013
  • Published electronically: March 25, 2014
  • Additional Notes: The first author was supported by the EPSRC, Project No EP/H026568/1 and by Magdalen College, Oxford.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 27 (2014), 1117-1145
  • MSC (2010): Primary 20C33; Secondary 18E30, 20C20
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00791-8
  • MathSciNet review: 3230819