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arXiv · 0808.2729

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

Avraham Aizenbud·Dmitry Gourevitch
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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), $$dim Hom_{GL(n,F)}(π,τ) \leq 1.$$ For p-adic fields those results were proven in [AGRS].

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Avraham Aizenbud, Dmitry Gourevitch. 2008-08-20. Multiplicity one theorem for (GL(n+1,R),GL(n,R)). https://doi.org/10.1007/s00029-009-0544-7

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