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Affine Weyl group multiple Dirichlet series: type $\widetilde{A}$

Part of: Linear algebraic groups and related topics Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  08 November 2016

Ian Whitehead
Ian Whitehead*
Affiliation:
School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA email iwhitehe@umn.edu
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Abstract

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We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac–Moody root system $\widetilde{A}_{n}$, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is over the rational function field $\mathbb{F}_{q}(t)$, and is based upon four natural axioms from algebraic geometry. We prove that the four axioms yield a unique series with meromorphic continuation to the largest possible domain and the desired infinite group of symmetries.

Keywords

multiple Dirichlet seriesaffine Kac–Moody groups

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 20G44: Kac-Moody groups
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 12 , December 2016 , pp. 2503 - 2523
Copyright
© The Author 2016 

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