Related papers: Weyl group multiple Dirichlet series of type C

Weyl group multiple Dirichlet series, introduced by Brubaker, Bump, Chinta, Friedberg and Hoffstein, are expected to be Whittaker coefficients of Eisenstein series on metaplectic groups. Chinta and Gunnells constructed these multiple…

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…

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…

We computed the first Whittaker coefficient of an Eisenstein series on a global metaplectic group induced from the torus and related the result with a Weyl group multiple Dirichlet series attached to the (dual) root system of the group…

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…

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…

We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A series given by Brubaker, Bump, Friedberg,…

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…

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 construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are…

In this paper we provide an explicit construction of a $distinctive$ multiple Dirichlet series associated to products of quadratic Dirichlet L-series, which we believe should be tightly connected to a generalized metaplectic Whittaker…

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}…

Motivated by work of Kac and Lusztig, we define a root system and a Weyl groupoid for a large class of semisimple Yetter-Drinfeld modules over an arbitrary Hopf algebra. The obtained combinatorial structure fits perfectly into an existing…

We study the structure of $p$-parts of Weyl group multiple Dirichlet series. In particular, we extend results of Chinta, Friedberg, and Gunnells and show, in the stable case, that the $p$-parts of Chinta and Gunnells agree with those…

We use techniques from statistical mechanics to provide new formulas for Whittaker coefficients of metaplectic Eisenstein series on odd orthogonal groups, matching Friedberg and Zhang. We study a particular variation/generalization of the…

Let $\mathcal{D}$ be a Dynkin diagram and let $\Pi=\{\alpha_1,\dots ,\alpha_{\ell}\}$ be the simple roots of the corresponding Kac--Moody root system. Let $\mathfrak{h}$ denote the Cartan subalgebra, let $W$ denote the Weyl group and let…

We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the $n$-fold cover of the split odd orthogonal group $SO_{2r+1}$. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured…

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…

We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However…

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…