A crystal definition for symplectic multiple dirichlet series

We present a definition for Weyl group multiple Dirichlet series (MDS) of Cartan type C, where the coefficients of the series are given by statistics on crystal graphs for certain highest-weight representations of Sp(2r, C). In earlier work (Beineke et al., Pacific J. Math., 2011), we presented a definition based on Gelfand-Tsetlin patterns, and the equivalence of the two definitions is explained here. Finally, we demonstrate how to prove analytic continuation and functional equations for any multiple Dirichlet series with fixed data by reduction to rank one information. This method is amenable to MDS of all types.