Yangians, finite W-algebras and the Non Linear Schrodinger hierarchy

TL;DR

This paper establishes a connection between Yangians and finite W-algebras, illustrating this relationship through the Non Linear Schrödinger hierarchy and providing explicit realizations of generators via deformed oscillators.

Contribution

It introduces an algebra morphism linking Yangians and finite W-algebras and demonstrates this in the context of the Non Linear Schrödinger hierarchy with explicit generator realizations.

Findings

Established an algebra morphism between Yangians and finite W-algebras

Illustrated the correspondence within the Non Linear Schrödinger hierarchy

Provided explicit realizations of Yangian generators using deformed oscillators

Abstract

We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian generators in terms of deformed oscillators.