Metaplectic covers of Kac–Moody groups and Whittaker functions

Abstract

Starting from some linear algebraic data (a Weyl group invariant bilinear form) and some arithmetic data (a bilinear Steinberg symbol), we construct a central extension 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.