Multiplicity One Theorems and Invariant Distributions

Dmitry Gourevitch

Multiplicity One Theorems and Invariant Distributions

Representation Theory 2009-07-07 v1

Authors: Dmitry Gourevitch

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 $dim Hom_{GL(n,F)}(\pi,\rho)\leq 1.$

Keywords

automorphic representations group representations representation theory of groups

Cite

@article{arxiv.0907.0965,
  title  = {Multiplicity One Theorems and Invariant Distributions},
  author = {Dmitry Gourevitch},
  journal= {arXiv preprint arXiv:0907.0965},
  year   = {2009}
}

Comments

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

Multiplicity One Theorems and Invariant Distributions

Abstract

Keywords

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