Unramified Whittaker Functions on p-adic Loop Groups

TL;DR

This paper extends the theory of Whittaker functions to p-adic loop groups, establishing a Casselman-Shalika type formula for unramified cases, advancing the understanding of automorphic forms on infinite-dimensional groups.

Contribution

It introduces unramified Whittaker functions on p-adic affine Kac-Moody groups and proves an analogue of the Casselman-Shalika formula for these functions.

Findings

Defined unramified Whittaker functions on p-adic affine Kac-Moody groups

Established a Casselman-Shalika type formula for these functions

Extended classical results to infinite-dimensional group settings

Abstract

We define unramified Whittaker functions on the p-adic points of an affine Kac-Moody group, and establish an analogue of the Casselman-Shalika formula for these functions.