On certain multiplicity one theorems
Representation Theory
2007-05-23 v1 Number Theory
Abstract
We prove several multiplicity one theorems in this paper. For k a local field not of characteristic two, and V a symplectic space over k, 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), where V is an orthogonal space over k. 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).
Cite
@article{arxiv.math/0410002,
title = {On certain multiplicity one theorems},
author = {Jeffrey D. Adler and Dipendra Prasad},
journal= {arXiv preprint arXiv:math/0410002},
year = {2007}
}