A Gelfand--Graev representation of a finite reductive group G is obtained by inducing from a certain representation of a maximal unipotent subgroup of G. Gelfand--Graev representations can be used to classify certain irreducible representations of G. By considering other unipotent subgroups of G, we can recover more irreducible representations of G. I will construct a generalization of the Gelfand--Graev representation and look at some applications.
Generalized Gelfand-Graev Representations