Fourier-Jacobi models for real symplectic-metaplectic groups: the basic case

TL;DR

This paper extends existing methods to real symplectic-metaplectic groups, proving a key case of the local Gan-Gross-Prasad conjecture for Fourier-Jacobi models, building on prior work on Bessel models.

Contribution

It generalizes the approach of Gan-Ichino and Atobe to real fields and establishes the basic tempered case of the conjecture for Fourier-Jacobi models.

Findings

Proved the basic tempered case of the local Gan-Gross-Prasad conjecture for Fourier-Jacobi models.

Extended methods to real symplectic-metaplectic groups.

Built on prior results for Bessel models by Chen-Luo.

Abstract

In this paper, we generalize the method of Gan-Ichino and Atobe in [GI16][A18] to the field of real numbers and prove the basic tempered case of the local Gan-Gross-Prasad conjecture for Fourier-Jacobi models of symplectic-metaplectic groups, based on the tempered case of the conjecture for Bessel models proved in [CL22] by Chen-Luo.