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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


From conjugacy classes in the Weyl group to unipotent classes, II
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by G. Lusztig
Represent. Theory 16 (2012), 189-211
Published electronically: April 3, 2012


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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Bibliographic 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:
  • MathSciNet review: 2904567