A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schr\"odinger Model

TL;DR

This paper introduces a non-symmetric Yang-Baxter algebra framework for the quantum nonlinear Schrödinger model, extending the algebraic structures and wavefunction generation methods beyond symmetric cases.

Contribution

It develops a non-symmetric algebraic approach using a vertex operator formalism and generalizes Yang-Baxter relations for the quantum nonlinear Schrödinger model.

Findings

Construction of non-symmetric wavefunctions using vertex operators

Generalization of Yang-Baxter relations to non-symmetric case

Linking non-symmetric functions with degenerate affine Hecke algebra

Abstract

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schr\"odinger model, introduced by Komori and Hikami using Gutkin's propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.