Supercharacters of Unipotent and Solvable Groups

Abstract

The notion of the supercharacter theory was introduced by P. Diaconis and I. M. Isaaks in 2008. In this paper, we present a review of the main notions and facts of the general theory and discuss the construction of the supercharacter theory for algebra groups and the theory of basic characters for unitriangular groups over a finite field. Based on his earlier papers, the author constructs the supercharacter theory for finite groups of triangular type. The structure of the Hopf algebra of supercharacters for triangular groups over finite fields is also characterized.