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 we obtain the notion of -fold metaplectic covers of Kac–Moody groups. In this setting, we prove a Casselman–Shalika-type formula for Whittaker functions.
"Metaplectic covers of Kac–Moody groups and Whittaker functions." Duke Math. J. 168 (4) 553 - 653, 15 March 2019. https://doi.org/10.1215/00127094-2018-0049