Let G be a simple algebraic group over an algebraically closed field of characteristic zero or positive odd, good characteristic. Let B be a Borel subgroup of G. We show that the spherical conjugacy classes of G intersect only the double cosets of B in G corresponding to involutions in the Weyl group of G. This result is used in order to prove that for a spherical conjugacy class O with dense B-orbit v(0). BwB there holds l(w) + rk(1-w) = dim O extending to the case of groups over fields of odd, good characteristic a characterization of spherical conjugacy classes obtained by Cantarini, Costantini and the author.

Spherical conjugacy classes and involutions in the Weyl group

CARNOVALE, GIOVANNA
2008

Abstract

Let G be a simple algebraic group over an algebraically closed field of characteristic zero or positive odd, good characteristic. Let B be a Borel subgroup of G. We show that the spherical conjugacy classes of G intersect only the double cosets of B in G corresponding to involutions in the Weyl group of G. This result is used in order to prove that for a spherical conjugacy class O with dense B-orbit v(0). BwB there holds l(w) + rk(1-w) = dim O extending to the case of groups over fields of odd, good characteristic a characterization of spherical conjugacy classes obtained by Cantarini, Costantini and the author.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2265776
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