Parahoric Subgroups and Supercuspidal Representations of p-Adic groups

JOINT IAS/PU NUMBER THEORY SEMINAR
Topic:Parahoric Subgroups and Supercuspidal Representations of p-Adic groups
Speaker:Dick Gross
Affiliation:Harvard University
Date:Thursday, December 9
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/nt/gross

This is a report on some joint work with Mark Reeder and Jiu-Kang Yu. I will review the theory of parahoric subgroups and consider the induced representation of a one-dimensional character of the pro-unipotent radical. A surprising fact is that this induced representation can (in certain situations) have finite length. I will describe the parahorics and characters for which this occurs, and what the Langlands parameters of the corresponding irreducible summands must be.