Duke Mathematical Journal

Metaplectic covers of Kac–Moody groups and Whittaker functions

Manish M. Patnaik and 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 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.

Article information

Source
Duke Math. J., Volume 168, Number 4 (2019), 553-653.

Dates
Received: 12 June 2017
Revised: 18 August 2018
First available in Project Euclid: 8 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1549594819

Digital Object Identifier
doi:10.1215/00127094-2018-0049

Mathematical Reviews number (MathSciNet)
MR3916064

Subjects
Primary: 20G44: Kac-Moody groups
Secondary: 11F68: Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series

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

Citation

Patnaik, Manish M.; Puskás, Anna. Metaplectic covers of Kac–Moody groups and Whittaker functions. Duke Math. J. 168 (2019), no. 4, 553--653. doi:10.1215/00127094-2018-0049. https://projecteuclid.org/euclid.dmj/1549594819


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