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We prove the local Gan-Gross-Prasad conjecture for the symplectic-metaplecticcase under some assumptions. This is the last case of the localGan-Gross-Prasad conjectures. We also prove two of Prasad's conjectures on thelocal theta correspondence in the almost equal rank case.

The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case