On an analogue of the Ichino-Ikeda conjecture for Whittaker coefficients on the metaplectic group

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 p-adic case, and hence the global conjecture under simplifying conditions at the archimedean places.