Multiplicity one theorem for (GL(n+1,R),GL(n,R))

2008/08/20 by Avraham Aizenbud, Dmitry Gourevitch · 1 citation
Mathematics · #math.RT #msc:20G05 #msc:22E45 #msc:20C99 #msc:46F10

paper · pdf · doi:10.1007/s00029-009-0544-7

published as Selecta Mathematica Volume 15, Number 2 / August, 2009 · 21 pages

arxiv created 2008/08/20 · arxiv updated 2009/12/01

Abstract

Let F be either R or C. Consider the standard embedding GL(n,F)<GL(n+1,F) and the action of GL(n,F) on GL(n+1,F) by conjugation. In this paper we show that any GL(n,F)-invariant distribution on GL(n+1,F) is invariant with respect to transposition. We show that this implies that for any irreducible admissible smooth Frechet representations π of GL(n+1,F) and τ of GL(n,F), dim Hom_GL(n,F)(π,τ) ≤ 1. For p-adic fields those results were proven in [AGRS].

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