Higher level Fock spaces and affine Yangian

TL;DR

This paper extends the action of the affine Yangian of type A to higher level Fock spaces, building on finite type A actions, and relates to quantum toroidal algebra actions on q-deformed Fock spaces.

Contribution

It introduces a new construction of affine Yangian actions on higher level Fock spaces, generalizing previous finite type A actions and connecting to quantum toroidal algebra results.

Findings

Constructed affine Yangian actions on higher level Fock spaces.

Extended known finite type A Yangian actions to affine case.

Related to quantum toroidal algebra actions on q-deformed Fock spaces.

Abstract

We construct actions of the affine Yangian of type A on higher level Fock spaces by extending known actions of the Yangian of finite type A due to Uglov. This is a degenerate analog of a result by Takemura-Uglov, which constructed actions of the quantum toroidal algebra on higher level $q$-deformed Fock spaces.