Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Katsylo theorem for sheets of spherical conjugacy classes   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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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph