We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system Ãn, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is over the rational function field Fq(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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© The Author 2016.
- affine Kac-Moody groups
- multiple Dirichlet series