Tung Le

Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

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 finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.

On the characters of the Sylow -subgroups of untwisted Chevalley groups

Let

A dual version of Huppert's conjecture on conjugacy class sizes

UY_n(q)

On the automorphisms of designs constructed from finite simple groups

be a Sylow p-subgroup of an untwisted Chevalley group

On a generalization of M-group

Y_n(q)

On the Character Degrees of Suzuki p-Groups of Type A and C

of rank n defined over

On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E

\mathbb{F}_q

Constructing characters of Sylow p-subgroups of finite Chevalley groups

where q is a power of a prime p. We partition the set

The irreducible characters of the Sylow

Irr(UY_n(q))

p

of irreducible characters of