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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.

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From conjugacy classes in the Weyl group to unipotent classes, III
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by G. Lusztig
Represent. Theory 16 (2012), 450-488
Published electronically: September 7, 2012


Let $G$ be an affine algebraic group over an algebraically closed field whose identity component $G^{0}$ is reductive. Let $W$ be the Weyl group of $G$ and let $D$ be a connected component of $G$ whose image in $G/G^{0}$ is unipotent. In this paper we define a map from the set of “twisted conjugacy classes” in $W$ to the set of unipotent $G^{0}$-conjugacy classes in $D$ generalizing an earlier construction which applied when $G$ is connected.
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Bibliographic Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Received by editor(s): October 13, 2011
  • Received by editor(s) in revised form: May 11, 2012
  • Published electronically: September 7, 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), 450-488
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 2968566