Multiplicity one theorems for Fourier-Jacobi models

For every genuine irreducible admissible smooth representation $π$ of the metaplectic group $\widetilde{\Sp}(2n)$ over a p-adic field, and every smooth oscillator representation $ω_ψ$ of $\widetilde{\Sp}(2n)$, we prove that the tensor product $π\otimes ω_ψ$ is multiplicity free as a smooth representation of the symplectic group $\Sp(2n)$. Similar results are proved for general linear groups and unitary groups.

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