Abstract
In the local, characteristic $0$, non-Archimedean case, we consider distributions on ${\rm GL}(n+1)$ which are invariant under the adjoint action of ${\rm GL}(n)$. We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from ${\rm GL}(n+1)$ to ${\rm GL}(n)$. Similar theorems are obtained for orthogonal or unitary groups.
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@misc{AG,
author={Aizenbud, Avraham and Gourevitch, Dmitry},
TITLE={A proof of the multiplicity one conjecture for $\mathrm{GL}(n)$ in $\mathrm{GL}(n + 1)$},
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