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Multiplicity one theorems for Fourier-Jacobi models
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 6, December 2012
- pp. 1655-1678
- 10.1353/ajm.2012.0044
- Article
- Additional Information
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.