Uniqueness of Whittaker model for the metaplectic group

Let F be a local nonarchimedean field. We prove the uniqueness of the Whittaker model for irreducible admissible representations of Sp_2n(F), the metaplectic double cover of Sp_2n(F). An ingredient of the proof is an explicit extension of Rao's normalized cocycle from Sp_2n(F) to GSp_2n(F).