Let U(q) denote the set of infinite nilpotent matrices over the finite field with q elements, called infinite unitriangular group. It is a wild group (not type I), thus the irreducible representation do not admit any reasonable parametrization. Nevertheless the set of all characters (positive definite, normalized class functions) characterize up to quasiequivalence representations of type I and II, therefore, they are our main object of study. The goal of this talk is to define what are SupercharacterTheories for U(q) and describe one in particular. This description relies on set partitions and some combinatorial relations.
