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

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.

28 pages. Comments more than welcome. This is the first of three papers based on the author's thesis: http://arxiv.org/abs/1406.0573

References in corpus (2)

• Weyl group multiple Dirichlet series constructed from quadratic characters
• Eisenstein Series on Covers of Odd Orthogonal Groups

Cited by in corpus (3)

• Metaplectic Covers of Kac-Moody Groups and Whittaker Functions
• Whittaker functions on metaplectic covers of GL(r)
• Moduli of Hyperelliptic Curves and Multiple Dirichlet Series