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Representation Theory

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

Author: G. Lusztig
Journal: Represent. Theory 16 (2012), 189-211
MSC (2010): Primary 20G99
Published electronically: April 3, 2012
MathSciNet review: 2904567
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Abstract: Let $G$ be a connected reductive group over an algebraically closed field of characteristic $p$. In an earlier paper we defined a surjective map $\Phi _{p}$ from the set $\underline {W}$ of conjugacy classes in the Weyl group $W$ to the set of unipotent classes in $G$. Here we prove three results for $\Phi _{p}$. First we show that $\Phi _{p}$ has a canonical one-sided inverse. Next we show that $\Phi _{0}=r\Phi _{p}$ for a unique map $r$. Finally, we construct a natural surjective map from $\underline {W}$ to the set of special representations of $W$ which is the composition of $\Phi _{0}$ with another natural map and we show that this map depends only on the Coxeter group structure of $W$.

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Additional Information

G. Lusztig
Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
MR Author ID: 117100

Received by editor(s): May 4, 2011
Received by editor(s) in revised form: July 19, 2011
Published electronically: April 3, 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.