Supercharacters for the finite groups of triangular type

TL;DR

This paper develops a supercharacter theory for finite groups of triangular type, generalizing previous theories for algebra groups and proving an analog of Kirillov's formula for these supercharacters.

Contribution

It introduces a new supercharacter theory for finite groups of triangular type, extending existing frameworks and establishing a Kirillov-like formula for supercharacters.

Findings

Constructed supercharacter theory for groups of triangular type

Generalized supercharacter theory for algebra groups

Proved supercharacter analog of Kirillov's formula

Abstract

We construct the supercharacter theory for the finite groups of triangular type. Its special case is the supercharacter theory for algebra groups of P.Diaconis and I.M.Isaacs. The supercharacter analog of the A.A. Kirillov formula for irreducible characters is proved.