Unramified whittaker functions on the metaplectic group

Kazhdan (unpublished), Shintani [Sh] and Casselman and Shalika [CS] computed explicitly the unramified Whittaker function of a quasisplit p-adic group. This is the main local ingredient used in the Rankin-Selberg-Shimura method, which yielded interesting results in the study of Euler products such as L(s,π ⊗π,) by Jacquet and Shalika [JS] (here π,π, are cuspidal GL(n, A_F)-modules), and L(s,π, r) by [F] (here π is a cuspidal GL(n, A_F)-module, E is a quadratic extension of the global field F, and r is the twisted tensor representation of the dual group of Res_E/F GL(n)). Our purpose here is to generalize Shintani's computation [Sh] from the context of GL(n) to that of the metaplectic r-fold covering group G of GL(n) (see [F', FK]).