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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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Elliptic elements in a Weyl group: a homogeneity property
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by G. Lusztig PDF
Represent. Theory 16 (2012), 127-151 Request permission


Let $G$ be a reductive group over an algebraically closed field whose characteristic is not a bad prime for $G$. Let $w$ be an elliptic element of the Weyl group which has minimum length in its conjugacy class. We show that there exists a unique unipotent class $X$ in $G$ such that the following holds: if $V$ is the variety of pairs $(g,B)$ where $g\in X$ and $B$ is a Borel subgroup such that $B,gBg^{-1}$ are in relative position $w$, then $V$ is a homogeneous $G$-space.
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Received by editor(s): January 13, 2011
  • Received by editor(s) in revised form: June 17, 2011
  • Published electronically: February 20, 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), 127-151
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 2888173