Supercharacter theory for the Borel contraction of the group GL(n, Fq)

Abstract

The notion of a supercharacter theory was introduсed by P. Diaconis and I.M. Isaacs in 2008. A supercharacter theory for a given finite group is a pair of a system of certain complex characters of the group and its partition into classes that have properties similar to the irreducible characters and conjugacy classes. In the present paper, we consider the group obtained by a group contraction from the general linear group over a finite field. For this group, we construct a supercharacter theory. In terms of rook placements, we classify supercharacters and superclasses, calculate values of supercharacters on superclasses.