Metaplectic Whittaker functions and crystal bases

We study Whittaker functions on nonlinear coverings of simple algebraic groups over a nonarchimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph and show that in type A, these expressions agree with known formulae for the prime-pow...

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Bibliographic Details
Published in:	Duke mathematical journal Vol. 156; no. 1; pp. 1 - 31
Main Author:	McNamara, Peter J.
Format:	Journal Article
Language:	English
Published:	DUKE University Press 15-01-2011 Duke University Press
Subjects:	11F70 22E50 automorphic representations over local and global fields Representation-theoretic methods Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Online Access:	Get full text
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Summary:	We study Whittaker functions on nonlinear coverings of simple algebraic groups over a nonarchimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph and show that in type A, these expressions agree with known formulae for the prime-power-supported coefficients of multiple Dirichlet series.
Bibliography:	doi:10.1215/00127094-2010-064 zbl:1217.22015 ark:/67375/765-GDB93D34-V pe:euclid.dmj/1292509116 istex:16D7D4674266154DFE52E9783CA00BA890F84FF7 pii:00127094-2010-064 mr:2746386
ISSN:	0012-7094 1547-7398
DOI:	10.1215/00127094-2010-064