Multiplicity One Theorems and Invariant Distributions

2009/07/06 by Gourevitch, Dmitry
#14L24 #14L30 #20C99 #20G05 #22E45 #22E50 #46F10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0907.0965

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)≤ 1.

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• Multiplicity one Conjectures
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