English

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

Number Theory 2019-02-20 v1

Abstract

We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system A~n\tilde{A}_n, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is over the rational function field Fq(t)\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

Cite

@article{arxiv.1408.0937,
  title  = {Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$},
  author = {Ian Whitehead},
  journal= {arXiv preprint arXiv:1408.0937},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-22T05:20:39.206Z