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.

Previous version had title "On the Casselman-Shalika formula for metaplectic groups"

References in corpus (3)

• The Langlands-Weissman Program for Brylinski-Deligne extensions
• Whittaker functions on metaplectic covers of GL(r)
• Metaplectic Demazure operators and Whittaker functions

Cited by in corpus (5)

• Metaplectic Covers of Kac-Moody Groups and Whittaker Functions
• Whittaker functions on metaplectic covers of GL(r)
• Moduli of Hyperelliptic Curves and Multiple Dirichlet Series
• Metaplectic Iwahori Whittaker functions and supersymmetric lattice models
• Hecke Modules from Metaplectic Ice