We study certain sums of irreducible characters and compatible unions of conjugacy classes
in finite algebra groups. These groups generalize the unimodular upper triangular groups …

We identify two seemingly disparate structures: supercharacters, a useful way of doing
Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a …

Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain
approximations to the ordinary character theory of the group. We make explicit the …

The general linear group [special characters omitted] over a field [special characters omitted]
contains a particularly prominent subgroup, the unipotent linear group [special characters …

Let K be an arbitrary field and let n be a positive integer. Let Un K denote the (upper)
unitriangular group of degree n over K; then Un K consists of all unipotent upper-triangular …

Let $ U_ {n}(q) $ denote the (upper) unitriangular group of degree $ n $ over the finite field
$\mathbb {F} _ {q} $ with $ q $ elements. In this paper we consider the basic (complex) …

Let K be an algebraically closed field of arbitrary characteristic and let n be a positive
integer. If K has prime characteristic p, we will assume that p> n. Let U,(K) denote the (upper) …

Let G be the group of n× n upper-triangular matrices with elements in a finite field and ones
on the diagonal. This paper applies the character theory of Andre, Carter, and Yan to …

The theory of supercharacters, recently developed by Diaconis-Isaacs and André, is used to
derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently …

C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable
substitute for character theory in wild groups such as the unipotent uppertriangular group …