Deformed oscillators algebra formulation of the Nonlinear Schrodinger hierarchy and of its symmetry

TL;DR

This paper develops a formulation of the Nonlinear Schrödinger hierarchy using deformed oscillator algebra, revealing its Yangian symmetry and connecting it to finite W-algebras, thus providing a new algebraic perspective.

Contribution

It introduces a novel algebraic framework for the Nonlinear Schrödinger hierarchy based on deformed oscillator algebra, linking Yangian and W-algebras.

Findings

Formulation of the hierarchy using deformed oscillator algebra

Demonstration of Yangian symmetry within this framework

Connection established between Yangian Y(gl(N)) and finite W(gl(pN),N.gl(p)) algebras

Abstract

We present a self-contained formulation of the Nonlinear Schrodinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y(gl(N)) and finite W(gl(pN),N.gl(p)) algebras is also illustrated in this framework.