  A Weyl group multiple Dirichlet series is a Dirichlet series in several
complex variables attached to a root system Phi. The number of variables equals
the rank r of the root system, and the series satisfies a group of functional
equations isomorphic to the Weyl group W of Phi. In this paper we construct a
Weyl group multiple Dirichlet series over the rational function field using
n-th order Gauss sums attached to the root system of type A_2. The basic
technique is to construct a rational function in r variables invariant under a
certain action of W, and use this to build a ``local factor'' of the global
series.
