On Branching Laws For Representations Of GL sub(4)(F) To Sp sub(4)(F)

Abstract

This thesis analyzes representations of the form Ind sub(P) exp(GL sub(4)(F)) sigma sub(1) (X) sigma sub(2) when restricted to Sp sub(4)(F) where the sigma sub(i) are supercuspidal representations of GL sub(2)(F). The main result classifes 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 invariants are shown to have geometric interpretations in the building.