Multiplicity one theorems for Fourier-Jacobi models

Details Multiplicity one theorems for Fourier-Jacobi models Multiplicity one theorems for Fourier-Jacobi models

2009-03-08

arxiv.org/abs/0903.1417v2

Mathematics

Representation Theory

Scientific paper

For every genuine irreducible admissible smooth representation $\pi$ of the metaplectic group $\widetilde{\Sp}(2n)$ over a p-adic field, and every smooth oscillator representation $\omega_\psi$ of $\widetilde{\Sp}(2n)$, we prove that the tensor product $\pi\otimes \omega_\psi$ 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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