Affine Weyl group multiple Dirichlet series: Type Ã

Ian Whitehead

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3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2503-2523
Number of pages21
JournalCompositio Mathematica
Issue number12
StatePublished - Dec 1 2016

Bibliographical note

Publisher Copyright:
© The Author 2016.


  • affine Kac-Moody groups
  • multiple Dirichlet series


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