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 …

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 …

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) …

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 …

It is becoming increasingly clear that the supercharacter theory of the finite group of
unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions …

We build, from the collection of all groups of unitriangular matrices, Hopf monoids in Joyal's
category of species. Such structure is carried by the collection of class function spaces on …

In studying the enumerative theory of super characters of the group of upper triangular
matrices over a finite field, we found that the moments (mean, variance, and higher …

Diaconis and Isaacs define in [8](Diaconis and Isaacs, 2008) a supercharacter theory for
algebra groups over a finite field by constructing certain unions of conjugacy classes called …

It is well known that the representation theory of the finite group of unipotent upper-triangular
matrices Un over a finite field is a wild problem. By instead considering approximately …

We study irreducible characters, and define and study supercharacters of the adjoint group
of a finite radical ring. We extend work of Halasi on irreducible characters, and recent work …