Metaplectic Covers of Kac-Moody Groups and Whittaker Functions
Representation Theory
2019-05-29 v1 Number Theory
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 -fold metaplectic covers of Kac-Moody groups. In this setting, we prove a Casselman-Shalika type formula for Whittaker functions.
Keywords
Cite
@article{arxiv.1703.05265,
title = {Metaplectic Covers of Kac-Moody Groups and Whittaker Functions},
author = {Manish Patnaik and Anna Puskás},
journal= {arXiv preprint arXiv:1703.05265},
year = {2019}
}