Classifying the irreducible characters of the group of unipotent upper triangular matrices over a finite field is a provably difficult problem. We can instead consider a coarsening of the usual character theory, which we will refer to as a supercharacter theory. I will construct a supercharacter theory of the group of unipotent upper triangular matrices and look at analogous constructions in other types.
Supercharacter Theories of Unipotent Groups