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Affine Weyl group multiple Dirichlet series: type $\widetilde{A}$
Published online by Cambridge University Press: 08 November 2016
Abstract
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.
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- Research Article
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- © The Author 2016
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