Spherical conjugacy classes and involutions in the Weyl group

2006/12/14 by Giovanna Carnovale, Carnovale, Giovanna
Mathematics · #14M15 #20G15 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0612408

openalex publication_date 2006/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 v₀ 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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