Affine Weyl group multiple Dirichlet series: type $\widetilde{A}$. (8th November 2016)

• Record Type: Journal Article
• Authors: Whitehead, Ian
• Is Part Of: Compositio mathematica. Volume 152:Number 12(2016)
• Page Start: 2503
• Page End: 2523
• Publication Date: 2016-11-08
• Subjects: 11M32 (primary), -- 20G44 (secondary); multiple Dirichlet series, -- affine Kac–Moody groups; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16007715
• Languages: English
• ISSNs: 0010-437X

Abstract

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.