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Spherical conjugacy classes and the Bruhat decomposition. (English) Zbl 1195.20051

Let \(G\) be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. The spherical conjugacy classes in \(G\) are characterized as those intersecting only Bruhat cells in \(G\) corresponding to involutions in the Weyl group of \(G\).

MSC:

20G15 Linear algebraic groups over arbitrary fields
20E45 Conjugacy classes for groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
14M17 Homogeneous spaces and generalizations
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References:

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