Multiplicity one theorems for Fourier-Jacobi models

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