On Iwahori-Whittaker Functions for Metaplectic Groups

TL;DR

This paper establishes a connection between Iwahori-Whittaker functions on metaplectic groups and Demazure-Lusztig operators, leading to an analogue of the Casselman-Shalika formula for spherical Whittaker functions.

Contribution

It introduces a novel relationship between Iwahori-Whittaker functions and Demazure-Lusztig operators in the metaplectic setting, extending classical formulas.

Findings

Derived an analogue of the Casselman-Shalika formula for metaplectic groups

Linked Iwahori-Whittaker functions to Demazure-Lusztig operators

Utilized combinatorial identities for operator sums

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.