Character Values of Finite Reductive Groups

Abstract: Reductive groups are an important class of groups that arise from the theory of algebraic groups. Their prominence in finite group theory comes from their close relationship to finite simple groups, which are the building blocks from which all finite groups are constructed. The principal example of a finite reductive group is the general linear group of invertible matrices defined over a finite field. The complex-irreducible characters of a finite group, which are certain complex-valued functions, are an essential tool in modern finite group theory. In this talk, I will present recent results concerning the values of these functions for finite reductive groups.