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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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From conjugacy classes in the Weyl group to unipotent classes, II
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by G. Lusztig PDF
Represent. Theory 16 (2012), 189-211 Request permission

Abstract:

Let $G$ be a connected reductive group over an algebraically closed field of characteristic $p$. In an earlier paper we defined a surjective map $\Phi _{p}$ from the set $\underline {W}$ of conjugacy classes in the Weyl group $W$ to the set of unipotent classes in $G$. Here we prove three results for $\Phi _{p}$. First we show that $\Phi _{p}$ has a canonical one-sided inverse. Next we show that $\Phi _{0}=r\Phi _{p}$ for a unique map $r$. Finally, we construct a natural surjective map from $\underline {W}$ to the set of special representations of $W$ which is the composition of $\Phi _{0}$ with another natural map and we show that this map depends only on the Coxeter group structure of $W$.
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Received by editor(s): May 4, 2011
  • Received by editor(s) in revised form: July 19, 2011
  • Published electronically: April 3, 2012
  • Additional Notes: Supported in part by the National Science Foundation
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 16 (2012), 189-211
  • MSC (2010): Primary 20G99
  • DOI: https://doi.org/10.1090/S1088-4165-2012-00411-3
  • MathSciNet review: 2904567