A geometric comparison between representations of real and p-adic groups

Abstract: In this talk, I will present a geometric comparison of representations of two pairs of real and p-adic groups: between GL$_n(\mathbb C)$ and GL$_m(\mathbb Q_p)$, and between U$(p,q)$ and Sp$(m,\mathbb Q_p)$ or SO$(m,\mathbb{Q}_p)$. The comparisons are achieved by constructing an open embedding between the Langlands parameter spaces. We will sketch the construction, describe some desired properties, and discuss applications to Arthur packets and unitary representations. This is based on joint work (partly ongoing) with Taiwang Deng, Chang Huang, and Bin Xu.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar