Spherical conjugacy classes and involutions in the Weyl group

Details Spherical conjugacy classes and involutions in the Weyl group Spherical conjugacy classes and involutions in the Weyl group

2006-12-14

arxiv.org/abs/math/0612408v2

Mathematics

Representation Theory

Lemma 3.8 had an incorrect proof and it is removed without effecting the main results of the paper. One reference is added

Scientific paper

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 to prove that for a spherical conjugacy class O with dense B-orbit v_0 contained in BwB there holds l(w)+rk(1-w)=dim(O) extending a characterization of spherical conjugacy classes obtained by N. Cantarini, M. Costantini and the author to the case of groups over fields of odd, good characteristic.

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