On a Dimension Formula for Twisted Spherical Conjugacy Classes in Semisimple Algebraic Groups

2010/01/22 by Lu, Jiang-Hua
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1001.4001

Abstract

Let G be a connected semisimple algebraic group over an algebraically closed field of characteristic zero, and let þ be an automorphism of G. We give a characterization of þ-twisted spherical conjugacy classes in G by a formula for their dimensions in terms of certain elements in the Weyl group of G, generalizing a result of N. Cantarini, G. Carnovale, and M. Costantini when þ is the identity automorphism. For G simple and þ an outer automorphism of G, we also classify the Weyl group elements that appear in the dimension formula.

Related

• Spherical conjugacy classes and involutions in the Weyl group
• Spherical twists and the center of autoequivalence groups of K3 surfaces
• Spherical twists, relations and the center of autoequivalence groups of K3 surfaces
• From conjugacy classes in the Weyl group to semisimple conjugacy classes
• Twisted conjugacy classes in Symplectic groups, Mapping class groups and Braid groups(including an Appendix written with Francois Dahmani)