Related papers: Metaplectic Ice

In a previous paper the first two named authors defined an action of a Weyl group on rational functions and used it to construct multiple Dirichlet series. These series are related to Whittaker functions on an n-fold metaplectic cover of a…

Let $\theta$ and $\theta'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $\theta\otimes\theta'$ is a (very large) representation of $GL_n$. We…

We introduce generalizations of type $C$ and $B$ ice models which were recently introduced by Ivanov and Brubaker-Bump-Chinta-Gunnells, and study in detail the partition functions of the models by using the quantum inverse scattering…

We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur functions. This gives rise to a natural family…

Let $\phi$ be an $L^2$-normalized spherical vector in an everywhere unramified cuspidal automorphic representation of $\mathrm{PGL}_n$ over $\mathbb{Q}$ with Laplace eigenvalue $\lambda_{\phi}$. We establish explicit estimates for various…

For an arbitrary split adjoint group we identify the unramified Whittaker space with the space of skew-invariant functions on the lattice of coweights and deduce from it the Casselman-Shalika formula.

We study the automorphic theta representation $\Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. This representation is obtained from the residues of Eisenstein series on this group. If $r$ is odd, $n\le r <2n$,…

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…

We explore combinatorial formulas for deformations of highest weight characters of the odd orthogonal group $SO(2n+1)$. Our goal is to represent these deformations of characters as partition functions of statistical mechanical models -- in…

In this paper, we consider an extended Kazakov-Migdal model defined on an arbitrary graph. The partition function of the model, which is expressed as the summation of all Wilson loops on the graph, turns out to be represented by the…

Recently we propose a class of infinite-dimensional integral representations of classical gl(n+1)-Whittaker functions and local Archimedean local L-factors using two-dimensional topological field theory framework. The local Archimedean…

In the literature, two main approaches have been used to establish explicit formulas or propagation formulas for Whittaker functions over Archimedean local fields: one based on Jacquet integrals, and the other on the analysis of systems of…

We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group $G$ over a nonarchimedean local field $F$.…

We use statistical mechanics -- variants of the six-vertex model in the plane studied by means of the Yang-Baxter equation -- to give new deformations of Weyl's character formula for classical groups of Cartan type B, C, and D, and a…

Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…

The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain…

In this succinct note, it is showed that a partition function of equivalent classes of hyperbolic surfaces can be connected to an Ising model located on the boundary of the Poincare disc, as hinted by Poincare's Uniformization theorem and…

We propose new explicit form of q-deformed Whittaker functions solving q-deformed gl(l+1)-Toda chains. In the limit q->1 constructed solutions reduce to classical class one gl(l+1)-Whittaker functions in the form proposed by Givental. An…

A {\em cyclic graph} is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model…

The purpose of this paper is to present a quantum statistical theory of 2-dimensional vortex gas based on the generalized Hamiltonian dynamics recently developed. The quantized spectrum is evaluated for a pair of vortex on the basis of the…