$www.math.cornell.edu$

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:

Birgit Speh

Research Area:

Representation theory of p-adic Lie groups

Abstract: This thesis analyzes representations of the form Ind_P^GL_4(F) σ₁ ⊗ σ₂ when restricted to SP₄(F) where the σ_i 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.