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arXiv · 0907.0965

Multiplicity One Theorems and Invariant Distributions

Dmitry Gourevitch
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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 $π$ is an irreducible admissible smooth representation of GL(n+1,F) and $ρ$ is an irreducible admissible smooth representation of GL(n,F) then $$dim Hom_{GL(n,F)}(π,ρ)\leq 1.$$

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Dmitry Gourevitch. 2009-07-06. Multiplicity One Theorems and Invariant Distributions. https://arxiv.org/abs/0907.0965

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