On Iwahori–Whittaker functions for metaplectic groups

Abstract

We relate Iwahori–Whittaker functions on metaplectic covers to certain Demazure–Lusztig operators, the latter of which are built from a Weyl group action previously considered by G. Chinta and P. Gunnells. Using a certain combinatorial identity for the sum of these Demazure–Lusztig operators, we obtain an analogue of the Casselman–Shalika formula for spherical Whittaker functions in this context.