Metaplectic Ice

Abstract

We study spherical Whittaker functions on a metaplectic cover of GL(r + 1) over a nonarchimedean local eld using lattice models from statistical mechanics. An explicit description of this Whittaker function was given in terms of Gelfand-Tsetlin patterns in [5, 17], and we translate this description into an expression of the values of the Whittaker function as partition functions of a six- vertex model. Properties of the Whittaker function may then be expressed in terms of the commutativity of row transfer matrices potentially amenable to proof using the Yang-Baxter equation. We give two examples of this: rst, the equivalence of two di erent Gelfand-Tsetlin de nitions, and second, the e ect of the Weyl group action on the Langlands parameters. The second example is closely connected with another construction of the metaplectic Whittaker function by averaging over a Weyl group action [9, 10].