Two supercharacter theories for the parabolic subgroups in orthogonal and symplectic groups

Abstract

We construct two supercharacter theories (in the sense of P. Diaconis and I.M. Isaacs) for the parabolic subgroups in orthogonal and symplectic groups. For each supercharacter theory, we obtain a supercharacter analog of the A.A.Kirillov formula for irreducible characters of finite unipotent groups.2000 Mathematics Subject Classification. 20C33, 05E10.

Supercharacters for parabolic contractions of finite groups of A,B,C,D Lie types

“…A supercharacter theory for the Sylow subgroups in the orthogonal and symplectic groups is constructed in [5,6,7,17]. The author proposed a supercharacter theory for parabolic subgroups in O(n) and Sp(n) in the paper [15]. This approach is developing in the present paper for parabolic contractions of orthogonal and symplectic groups.…”