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arXiv · 1408.0937

Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$

Ian Whitehead
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Abstract

We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system $\tilde{A}_n$, 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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Ian Whitehead. 2014-08-05. Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$. https://doi.org/10.1112/s0010437x16007715

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