Fourier-Jacobi models for real symplectic-metaplectic groups

The Gan–Gross–Prasad conjecture describes branching laws for representations of classical groups, predicting when certain Bessel or Fourier–Jacobi models exists and with what multiplicity in terms of Langlands parameters. In this talk, I will discuss the local Gan–Gross–Prasad conjecture in the Fourier–Jacobi case for real symplectic–metaplectic groups. We prove the conjecture in the basic tempered case by using theta correspondence to reduce the Fourier–Jacobi case to the Bessel case. This is joint work with Cheng Chen and Rui Chen.