A remarkable connection between Yangians and finite W-algebras

TL;DR

This paper establishes a significant link between finite W-algebras and Yangians, showing that many finite W-algebras satisfy Yangian relations, which aids in understanding their representations.

Contribution

It proves that a large class of finite W-algebras can be realized as Yangians, revealing a deep connection and enabling new approaches to their representation theory.

Findings

Finite W-algebras satisfy Yangian relations.

Finite W-algebras can be realized as Yangians.

This connection helps analyze W algebra representations.

Abstract

For a large class of finite W algebras, the defining relations of a Yangian are proved to be satisfied. Therefore such finite W algebras appear as realisations of Yangians. This result is useful to determine properties of such W algebra representations.