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arXiv · 1703.05265

Metaplectic Covers of Kac-Moody Groups and Whittaker Functions

Manish Patnaik·Anna Puskás
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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.

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BibTeXRIS

Manish Patnaik, Anna Puskás. 2017-03-15. Metaplectic Covers of Kac-Moody Groups and Whittaker Functions. https://doi.org/10.1215/00127094-2018-0049

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