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

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- Represent. Theory
**16**(2012), 189-211 Request permission

## 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 $W$.## References

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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
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**16**(2012), 189-211 - MSC (2010): Primary 20G99
- DOI: https://doi.org/10.1090/S1088-4165-2012-00411-3
- MathSciNet review: 2904567