Yangians and W-algebras

TL;DR

This paper explores the relationship between W-algebras and Yangians for gl(N), enabling R-matrix construction and classification of representations, with applications demonstrated in the nonlinear Schrödinger equation.

Contribution

It establishes a novel connection between W-algebras and Yangians, including twisted and super-Yangians, and applies this to representation theory and integrable systems.

Findings

Constructed R-matrices for W-algebras

Classified finite-dimensional irreducible representations

Applied results to nonlinear Schrödinger equation

Abstract

We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their finite-dimensional irreducible representations. We illustrate it in the framework of nonlinear Schroedinger equation in 1+1 dimension.