# Metaplectic Covers of Kac-Moody Groups and Whittaker Functions

## TL;DR

This paper constructs metaplectic covers of Kac-Moody groups using algebraic and arithmetic data, and establishes a Casselman-Shalika formula for Whittaker functions in this setting.

## Contribution

It introduces a new construction of metaplectic covers of Kac-Moody groups and derives a Casselman-Shalika type formula for their Whittaker functions.

## Key findings

- Construction of n-fold metaplectic covers of Kac-Moody groups
- Derivation of a Casselman-Shalika formula for Whittaker functions
- Generalization of previous work to infinite-dimensional Kac-Moody groups

## Abstract

Starting from some linear algebraic data (a Weyl-group invariant bilinear form) and some arithmetic data (a bilinear Steinberg symbol), we construct a cover of a Kac-Moody group generalizing the work of Matsumoto. Specializing our construction over non-archimedean local fields, for each positive integer n we obtain the notion of $n$-fold metaplectic covers of Kac-Moody groups. In this setting, we prove a Casselman-Shalika type formula for Whittaker functions.