Metaplectic Demazure operators and Whittaker functions

In a previous paper the first two named authors defined an action of a Weyl group on rational functions and used it to construct multiple Dirichlet series. These series are related to Whittaker functions on an n-fold metaplectic cover of a reductive group. In this paper, we define metaplectic analogues of the Demazure and Demazure-Lusztig operators. We show how these operators, together with results of McNamara, can be used to compute Whittaker functions on metaplectic groups over p-adic fields.