A Katsylo theorem for sheets of spherical conjugacy classes

Carnovale, Giovanna; Esposito, Francesco

doi:10.1090/ert/470

A Katsylo theorem for sheets of spherical conjugacy classes
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by Giovanna Carnovale and Francesco Esposito

Represent. Theory 19 (2015), 263-280

DOI: https://doi.org/10.1090/ert/470

Published electronically: November 2, 2015

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Abstract:

We show that, for a sheet or a Lusztig stratum $S$ containing spherical conjugacy classes in a connected reductive algebraic group $G$ over an algebraically closed field in good characteristic, the orbit space $S/G$ is isomorphic to the quotient of an affine subvariety of $G$ modulo the action of a finite abelian $2$-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of $G$. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smooth.

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