The use of simulation for high-dimensional intractable computations has revolutionized
applied mathematics. Designing, improving and understanding the new tools leads to (and …

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 …

In 1896, after correspondence with Dedekind, Frobenius published two papers in which
group character theory was introduced and was used to describe the factorization of the …

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 …

We define and study super-characters (over the complex field) of the classical finite
unipotent groups of types Bn, Cn and Dn. Under the assumption that the prime is sufficiently …

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 …