Related papers: Weyl group multiple Dirichlet series constructed f…

A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Phi. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations…

Let Phi be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s_1,...,s_r, initially converging for Re(s_i) sufficiently large, which has meromorphic continuation to…

Let Phi be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s_1,...,s_r, initially converging for Re(s_i) sufficiently large, that has meromorphic continuation to…

We develop the theory of Weyl group multiple Dirichlet series for root systems of type C. For an arbitrary root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and…

Weyl group multiple Dirichlet series are Dirichlet series in $r$ complex variables, with analytic continuation to $\mathbb{C}^r$ and a group of functional equations isomorphic to the Weyl group of a reduced root system of rank $r$. Such…

We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system $\tilde{A}_n$, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is…

Let $W$ be the Weyl group of a simply-laced affine Kac-Moody Lie group, excepting $\tilde{A}_n$ for $n$ even. We construct a multiple Dirichlet series $Z(x_1, \ldots x_{n+1})$, meromorphic in a half-space, satisfying a group $W$ of…

A multiple Dirichlet series in two variables is constructed as a Mellin transform of a higher order Eisenstein series. It is shown to extend to a meromorphic function and satisfy two independent functional equations.

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of…

In this paper and its sequel \cite{DPP}, we investigate the precise relationship between the quadratic affine Weyl group multiple Dirichlet series in the sense of \cite{CG1, BD}, and those defined axiomatically by Whitehead \cite{White2}…

In this article we study analytic properties of the multiple Dirichlet series associated to additive and Dirichlet characters. For the multiple Dirichlet series associated to additive characters, the meromorphic continuation is established…

We prove functional equations for multiple Dirichlet series defined by a collection of five geometric axioms. We find functional equations of two types: one modeled on the functional equations of Dirichlet $L$-functions, and another modeled…

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic…

This paper is concerned with the Weyl composition of symbols in large dimension. We specify a class of symbols in order to estimate the Weyl symbol of the product of two Weyl $h-$pseudodifferential operators, with constants independent of…

We define a multiple Dirichlet series associated with quadrics which is the zero locus of a quadratic form. This multiple Dirichlet series is linked to a Shintani zeta function associated with a prehomogeneous vector space. To obtain the…

In this article, we obtain the analytic continuation of the multiple shifted Lucas zeta function, multiple Lucas $L$-function associated to Dirichlet characters and additive characters. We then compute a complete list of exact singularities…

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

We give explicit formulas for the residue of the Chinta-Gunnells average attached to a finite irreducible root system, at the polar divisor corresponding to a simple short root. The formula describes the residue in terms of the average…

We give an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb F_q(T)$, generalizing a set of axioms given by Diaconu and Pasol. The key axiom, relating the coefficients at prime powers to sums of the…

Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_\lambda$ of F we assign a multiplet of irreducible representations of…