Towards a supercharacter theory for parabolic subgroups

A supercharacter theory is a system of characters of a finite group that afford a partition of the group obeying certain properties. The main example is the system of irreducible characters and the partition into conjugacy classes. For some groups, classification of irreducible characters turns out to be an extremely difficult problem. In this case, the main goal is to construct a supercharacter theory that is as close as possible to the theory of irreducible characters. In the talk, we present the supercharacter theories for certain unipotent and solvable groups, and for the parabolic subgroups in GL(n).