In previous papers we formulated an analogue of the Ichino–Ikeda conjectures for Whittaker–Fourier coefficients of automorphic forms on quasisplit classical groups and the metaplectic group of arbitrary rank. In the latter case we reduced the conjecture to a local identity. In this paper we prove the local identity in the -adic case, and hence the global conjecture under simplifying conditions at the archimedean places.
"On an analogue of the Ichino–Ikeda conjecture for Whittaker coefficients on the metaplectic group." Algebra Number Theory 11 (3) 713 - 765, 2017. https://doi.org/10.2140/ant.2017.11.713