A Katsylo theorem for sheets of spherical conjugacy classes
Representation Theory
2015-01-20 v1 Group Theory
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.
Cite
@article{arxiv.1501.04534,
title = {A Katsylo theorem for sheets of spherical conjugacy classes},
author = {Giovanna Carnovale and Francesco Esposito},
journal= {arXiv preprint arXiv:1501.04534},
year = {2015}
}