Multiplicity one theorems for Fourier-Jacobi models

DOI 5 Citations

Abstract

<jats:p xml:lang="en"> For every genuine irreducible admissible smooth representation $\pi$ of the metaplectic group $\widetilde{{\rm Sp}}(2n)$ over a $p$-adic field, and every smooth oscillator representation $\omega_\psi$ of $\widetilde{{\rm Sp}}(2n)$, we prove that the tensor product $\pi\otimes\omega_\psi$ is multiplicity free as a smooth representation of the symplectic group ${\rm Sp}(2n)$. Similar results are proved for general linear groups and unitary groups. </jats:p>

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