A supercharacter theory for involutive algebra groups

摘要

If J is a finite-dimensional nilpotent algebra over a finite field k, the algebra group P = 1 + J admits a (standard) supercharacter theory as defined in [16]. If J is endowed with an involution sigma, then sigma naturally defines a group automorphism of P = 1 + J, and we may consider the fixed point subgroup C-P (sigma) = {x is an element of P:sigma(x) = x(-1)}. Assuming that k has odd characteristic p, we use the standard supercharacter theory for P to construct a supercharacter theory for C-P(sigma). In particular, we obtain a supercharacter theory for the Sylow p-subgroups of the finite classical groups of Lie type, and thus extend in a uniform way the construction given by Andre and Neto in [7,8] for the special case of the symplectic and orthogonal groups. (C) 2015 Elsevier Inc. All rights reserved.