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Spherical conjugacy classes and involutions in the Weyl group

Giovanna Carnovale
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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 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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Giovanna Carnovale. 2007-01-11. Spherical conjugacy classes and involutions in the Weyl group. https://arxiv.org/abs/math/0612408

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