Generalized and degenerate Whittaker quotients and Fourier coefficients

The study of Whittaker models for representations of reductive groups over

local and global fields has become a central tool in representation theory and the theory of automorphic forms, though their Fourier coefficients.  We will start by recalling the classical results on the existence and uniqueness of such models.

In order to encompass representations that do not have Whittaker models, one attaches a degenerate (or a generalized) Whittaker model WO, or a Fourier coefficient in the global case, to any nilpotent orbit.  We will discuss the relation between different kinds of degenerate Whittaker models, and applications to the existence of these models.

We will give several examples for GLn, and discuss the relation to the Bernstein – Zelevinsky derivatives.