Spherical conjugacy classes and involutions in the Weyl group
Abstract
Description
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.
Lemma 3.8 had an incorrect proof and it is removed without effecting the main results of the paper. One reference is added
Lemma 3.8 had an incorrect proof and it is removed without effecting the main results of the paper. One reference is added