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

Lusztig, G.

doi:10.1090/S1088-4165-2012-00422-8

From conjugacy classes in the Weyl group to unipotent classes, III
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by G. Lusztig

Represent. Theory 16 (2012), 450-488

DOI: https://doi.org/10.1090/S1088-4165-2012-00422-8

Published electronically: September 7, 2012

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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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