The spherical metaplectic Whittaker function on the double cover of Sp (2r, F), where F is a nonarchimedean local field, is considered from several different points of view. Previously, an expression, similar to the Casselman-Shalika formula, had been given by Bump, Friedberg, and Hoffstein as a sum is over the Weyl group. It is shown that this coincides with the expression for the p-parts of Weyl group multiple Dirichlet series of type Br as defined by the averaging method of Chinta and Gunnells. Two conjectural expressions as sums over crystals of type B are given and another as the partition function of a free-fermionic six-vertex model system.
- Chinta-gunnells averaging method
- Crystal graph
- Metaplectic whittaker function
- Solvable lattice model
- Weyl group multiple dirichlet series