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15 March 2019 Metaplectic covers of Kac–Moody groups and Whittaker functions
Manish M. Patnaik, Anna Puskás
Duke Math. J. 168(4): 553-653 (15 March 2019). DOI: 10.1215/00127094-2018-0049

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.

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Manish M. Patnaik. Anna Puskás. "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

Information

Received: 12 June 2017; Revised: 18 August 2018; Published: 15 March 2019
First available in Project Euclid: 8 February 2019

zbMATH: 07055151
MathSciNet: MR3916064
Digital Object Identifier: 10.1215/00127094-2018-0049

Subjects:
Primary: 20G44
Secondary: 11F68

Keywords: Casselman–Shalika formula , Kac–Moody groups , metaplectic covers , multiple Dirichlet series , Whittaker functions

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 4 • 15 March 2019
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