## Lie Groups Seminar

Gautam Gopal KrishnanCornell University
Degenerate series representations for symplectic groups
Friday, September 17, 2021 - 3:45pm
Malott 406
Abstract: Parabolic induction is a well-known procedure for building new representations from old. In this talk, we will focus on degenerate series representations for real symplectic groups and use algebraic techniques to describe the composition factors of the induced modules obtained from the Siegel parabolic subgroup. The wave front set of the induced modules restricts the factors that can occur and provides a combinatorial way of thinking about these factors in terms of nilpotent orbits. The $\tau$-invariant and $\theta$-correspondence can be used to narrow down the list of factors which we will then illustrate for $Sp(4,\mathbb{R})$ and compute the Langlands parameters associated to the factors in the composition series.