Supercharacter Theory for the Borel Contraction of the Group GL(n, $${{\mathbb{F}}_{q}}$$)

Abstract

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