Manish Patnaik (University of Alberta)

(Joint work with Valentin Buciumas). We describe the space of Whittaker functions on the metaplectic cover of a p-adic group G as a module over certain Hecke algebras of G. This object has been studied for some time, influenced  both by the theory of multiple Dirichlet series and, more recently, by certain solvable lattice models. We explain how the Whittaker module can be expressed in terms of the quantum group at a root of unity attached to the Langlands dual group of G. To do this, we use certain metaplectic Demazure-Lusztig operators to develop a Gauss-sum twisted Kazhdan-Lusztig theory for the Whittaker spaces in question.  As an application, we deduce a ‘geometric’ Casselman-Shalika formula for metaplectic covers, conjectured in a slightly related form by S. Lysenko, and which was one of the main motivations for this work.