To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r variables, whose group of functional equations is isomorphic to… (More)

Preface An L-function, as the term is generally understood, is a Dirichlet series in one complex variable s with an Euler product that has (at least conjecturally) analytic continuation to all… (More)

Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th… (More)

Weyl group multiple Dirichlet series were associated with a root system Φ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker,… (More)

We develop the theory of “Weyl group multiple Dirichlet series” for root systems of type C. For a root system of rank r and a positive integer n, these are Dirichlet series in r complex variables… (More)

If F is a local field containing the group μn of n-th roots of unity, and if G is a split semisimple simply connected algebraic group, then Matsumoto [27] defined an n-fold covering group of G(F ),… (More)

We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map g 7→ R(g) from GL(2,C)×GL(1,C) to End(V ⊗V ) where V is a… (More)

We present a definition for Weyl group multiple Dirichlet series (MDS) of Cartan type C, where the coefficients of the series are given by statistics on crystal graphs for certain highest weight… (More)

We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple padic group, indexed by the Weyl group. We show… (More)

Weyl group multiple Dirichlet series were associated with a root system Φ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker,… (More)