Jonathan Needleman

Jonathan Needleman
Ph.D. (2009) Cornell University

First Position

Assistant professor at Oberlin College

Dissertation

On Branching Laws for Representations of GL4(F) to SP4(F)

Advisor:


Research Area:
Representation theory of p-adic Lie groups

Abstract: This thesis analyzes representations of the form IndPGL_4(F) σ1 ⊗ σ2 when restricted to SP4(F) where the σi are supercuspidal representations of GL2(F). The main result classifies all irreducible quotients of this restriction which are non-degenerate and parabolically induced. The second half of the thesis studies group actions on Euclidean buildings. This is intended to start the analysis of which supercuspidal representations appear in the quotient of the restricted representation. In studying these group actions various combinatorial invarients are shown to have geometric interpretations in the building.