On certain multiplicity one theorems

Abstract

We prove several multiplicity one theorems in this paper. Fork a local field not of characteristic two, and V a symplectic space overk, any irreducible admissible representation of the symplectic similitude group GSp(V) decomposes with multiplicity one when restricted to the symplectic group Sp(V). We prove the analogous result for GO(V) and O(V), whereV is an orthogonal space overk. When k is non-archimedean, we prove the uniqueness of Fourier-Jacobi models for representations of GSp(4), and the existence of such models for supercuspidal representations of GSp(4).