相关论文: Quantum inverse scattering method and generalizati…
The wavefunction of the free-fermion six-vertex model was found to give a natural realization of the Tokuyama combinatorial formula for the Schur polynomials by Bump-Brubaker-Friedberg. Recently, we studied the correspondence between the…
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…
We will give new applications of quantum groups to the study of spherical Whittaker functions on the metaplectic $n$-fold cover of $GL(r,F)$, where $F$ is a nonarchimedean local field. Earlier Brubaker, Bump, Friedberg, Chinta and Gunnells…
The purpose of this paper is to show that the quantum inverse scattering method for the so-called q-boson model has a nice interpretation in terms of the algebra of symmetric functions. In particular, in the case of the phase model…
We interpret values of spherical Whittaker functions on metaplectic covers of the general linear group over a nonarchimedean local field as partition functions of two different solvable lattice models. We prove the equality of these two…
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…
In this paper, we extend results connecting quantum groups to spherical Whittaker functions on metaplectic covers of $GL_r(F)$, for $F$ a nonarchimedean local field. Brubaker, Buciumas, and Bump showed that for a certain metaplectic…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current…
We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS). We…
Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are…
The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…
We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…
The $b$-Whittaker functions are eigenfunctions of the modular $q$-deformed $\mathfrak{gl}_n$ open Toda system introduced by Kharchev, Lebedev, and Semenov-Tian-Shansky. Using the quantum inverse scattering method, the named authors obtained…
The tetrahedron equation introduced by Zamolodchikov is a three-dimensional generalization of the Yang-Baxter equation. Several types of solutions to the tetrahedron equation that have connections to quantum groups can be viewed as…
We apply the Izergin-Korepin analysis to the study of the projected wavefunctions of the generalized free-fermion model. We introduce a generalization of the $L$-operator of the six-vertex model by Bump-Brubaker-Friedberg and…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…
Using the representation theory of $\frak{gl}(N,\RR)$, we express the wave function of the $GL(N,\RR)$ Toda chain, which two of us recently obtained by the Quantum Inverse Scattering Method, in terms of multiple integrals. The main tool is…
We examine and present new combinatorics for the Schur polynomials from the viewpoint of quantum integrability. We introduce and analyze an integrable six-vertex model which can be viewed as a certain degeneration model from a t-deformed…