Guay's affine Yangians and non-rectangular $W$-algebras

TL;DR

This paper constructs a homomorphism linking Guay's affine Yangian to non-rectangular W-algebras of type A, extending the algebra and coproduct structures to establish this connection.

Contribution

It introduces an extension of Guay's affine Yangian and its coproduct to map onto non-rectangular W-algebras, revealing new algebraic relationships.

Findings

Established a homomorphism between affine Yangian and W-algebras

Extended the algebraic structures to facilitate the homomorphism

Provided a new perspective on the algebraic structure of W-algebras

Abstract

We construct a non-trivial homomorphism from the Guay's affine Yangian to the universal enveloping algebra of non-rectangular $W$-algebras of type $A$. In order to construct the homomorphism, we extend the Guay's affine Yangian and its coproduct.