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Elliptic elements in a Weyl group: a homogeneity property

Author: G. Lusztig
Journal: Represent. Theory 16 (2012), 127-151
MSC (2010): Primary 20G99
Published electronically: February 20, 2012
MathSciNet review: 2888173
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Abstract: 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

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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.