Supercharacter theory for groups of invertible elements of reduced algebras

TL;DR

This paper develops a supercharacter theory for invertible elements in reduced algebras, providing explicit formulas for supercharacter values in the case of triangular groups.

Contribution

It introduces a new supercharacter framework for these groups and derives explicit formulas for supercharacter evaluations on superclasses.

Findings

Supercharacter theory constructed for invertible elements of reduced algebras.

Explicit formulas obtained for supercharacter values in triangular groups.

Enhanced understanding of representation theory for these algebraic groups.

Abstract

We construct a supercharacter theory for the group of invertible elements of a reduced algebra. For the case of the triangular group, we obtain the formula for values of supercharacters on superclasses.