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arXiv · 1501.04534

A Katsylo theorem for sheets of spherical conjugacy classes

Giovanna Carnovale·Francesco Esposito
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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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Giovanna Carnovale, Francesco Esposito. 2015-01-19. A Katsylo theorem for sheets of spherical conjugacy classes. https://arxiv.org/abs/1501.04534

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