Multiplicity One Theorems and Invariant Distributions

Abstract

This is my PhD thesis submitted to the Weizmann Institute of Science. It is based on the papers [AG08c], [AG08d], [AGRS07], [AGS08], [AGS09], [Aiz08] and [SZ08]. This thesis includes an introduction to Gelfand pairs and invariant distributions, a list of tools to work with invariant distributions oriented towards proving Gelfand property and a proof that the pair (GL(n+1,F),GL(n,F)) is a strong Gelfand pair. Namely, we prove that if $\pi$ is an irreducible admissible smooth representation of GL(n+1,F) and $\rho$ is an irreducible admissible smooth representation of GL(n,F) then $$dimHo{m}_{GL(n,F)}(\pi ,\rho )\le 1.$$

This is my PhD thesis submitted to the Weizmann Institute of Science. It is based on the papers arxiv:0812.5063v3, arXiv:0808.2729v1, arXiv:0709.4215v1, arXiv:0709.1273v4, arXiv:0711.1471, arXiv:0811.2768 and arXiv:0903.1413

References in corpus (5)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Schwartz functions on Nash manifolds
• (GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F
• Multiplicity one Conjectures
• A partial analog of integrability theorem for distributions on p-adic spaces and applications