We define the superclasses for a classical finite unipotent group U of type Bn (q), Cn (q), or
Dn (q), and show that, together with the supercharacters defined in [CAM André, AM Neto …

We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic
and unitary types. Our method utilizes group actions in a manner analogous to that of …

The “method of little groups” describes the irreducible characters of semidirect products with
abelian normal subgroups in terms of the irreducible characters of the factor groups. We …

If J is a finite-dimensional nilpotent algebra over a finite field k, the algebra group P= 1+ J
admits a (standard) supercharacter theory as defined in [16]. If J is endowed with an …

We construct supercharacter theories for a collection of unipotent matrix groups and produce
a Hopf monoid from the supercharacters. These supercharacter theories are coarser than …

A vector species is a functor from the category of finite sets with bijections to vector spaces;
informally, one can view this as a sequence of S_n S n-modules. A Hopf monoid (in the …

We provide a Hopf algebra structure on the space of superclass functions on the unipotent
upper triangular group of type D over a finite field based on a supercharacter theory …

Let UYn (q) be a Sylow p-subgroup of an untwisted Chevalley group Yn (q) of rank n defined
over Fq where q is a power of a prime p. We partition the set Irr (UYn (q)) of irreducible …

It is well known that the classification of irreducible characters for the group of upper
unitriangular nx n-matrices over a finite field with q elements, denoted U_n (q), is a" wild" …

A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero
elements of an abelian group $ A $. Inspired by the action of the linear characters of the …