Abstract
We establish the Fourier–Jacobi case of the local Gross–Prasad conjecture for unitary groups, by using local theta correspondence to relate the Fourier–Jacobi case with the Bessel case established by Beuzart-Plessis. To achieve this, we prove two conjectures of Prasad on the precise description of the local theta correspondence for (almost) equal rank unitary dual pairs in terms of the local Langlands correspondence. The proof uses Arthur’s multiplicity formula and thus is one of the first examples of a concrete application of this “global reciprocity law”.
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