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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems


Authors: Kyu-Hwan Lee and Yichao Zhang
Journal: Trans. Amer. Math. Soc. 367 (2015), 597-625
MSC (2010): Primary 11F68; Secondary 17B67
Published electronically: June 25, 2014
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Abstract: Weyl group multiple Dirichlet series, introduced by Brubaker, Bump, Chinta, Friedberg and Hoffstein, are expected to be Whittaker coefficients of Eisenstein series on metaplectic groups. Chinta and Gunnells constructed these multiple Dirichlet series for all the finite root systems using the method of averaging a Weyl group action on the field of rational functions. In this paper, we generalize Chinta and Gunnells' work and construct Weyl group multiple Dirichlet series for the root systems associated with symmetrizable Kac-Moody algebras, and establish their functional equations and meromorphic continuation.


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Additional Information

Kyu-Hwan Lee
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: khlee@math.uconn.edu

Yichao Zhang
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: yichao.zhang@uconn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06159-X
PII: S 0002-9947(2014)06159-X
Received by editor(s): October 10, 2012
Received by editor(s) in revised form: October 12, 2012, November 2, 2012, April 11, 2013, and April 21, 2013
Published electronically: June 25, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.