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Eisenstein series on loop groups


Author: Dongwen Liu
Journal: Trans. Amer. Math. Soc. 367 (2015), 2079-2135
MSC (2010): Primary 22E55; Secondary 22E65, 22E67
Published electronically: September 5, 2014
MathSciNet review: 3286509
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Abstract: Based on Garland's work, in this paper we construct the Eisenstein series on the adelic loop groups over a number field, induced from either a cusp form or a quasi-character which is assumed to be unramified. We compute the constant terms and prove their absolute and uniform convergence under the affine analog of Godement's criterion. For the case of quasi-characters the resulting formula is an affine Gindikin-Karpelevich formula. Then we prove the convergence of Eisenstein series themselves in certain analogs of Siegel subsets.


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Additional Information

Dongwen Liu
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: dongwen.liu@uconn.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06220-X
Keywords: Loop groups, Eisenstein series
Received by editor(s): April 19, 2012
Received by editor(s) in revised form: May 29, 2013
Published electronically: September 5, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.