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From conjugacy classes in the Weyl group to unipotent classes, III


Author: G. Lusztig
Journal: Represent. Theory 16 (2012), 450-488
MSC (2010): Primary 20G99
DOI: https://doi.org/10.1090/S1088-4165-2012-00422-8
Published electronically: September 7, 2012
MathSciNet review: 2968566
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Abstract: 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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Additional 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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.