Weyl Group Multiple Dirichlet Series for Symmetrizable Kac-Moody Root Systems

2012/10/11 by Kyu-Hwan Lee, Yichao Zhang, Lee, Kyu-Hwan +1
Mathematics · #11F68 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.NT #math.RA #math.RT #msc:11F68

paper · pdf · doi:10.48550/arxiv.1210.3310

35 pages

arxiv created 2013/04/23 · arxiv updated 2013/04/24

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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