Structure of degenerate principal series of exceptional groups
The reducibility and structure of parabolic inductions is a basic problem in the representation theory of p-adic groups. Of particular interest are principal series and degenerate principal series representations, that is parabolic induction of 1-dimensional representations of Levi subgroups.
In this talk, I will start by describing the functor of normalized induction and its left adjoint, the Jacquet functor, and by going through several examples in the group SL_4(Q_p) will describe an algorithm which can be used to determine reducibility of such representations.
This algorithm is the core of a joint project with Hezi Halawi, in which we study the structure of degenerate principal series of exceptional groups of type En (see https://arxiv.org/abs/1811.02974).