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Representation Theory

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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
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

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.