Several realizations of Fock modules for quantum toroidal algebras of sl(n)

TL;DR

This paper explores various realizations of Fock modules for quantum toroidal algebras of sl(n), connecting them to vertex, shuffle, and L-operator representations, extending known results from gl(1).

Contribution

It generalizes the relations between Fock modules and other representations from gl(1) to sl(n) quantum toroidal algebras.

Findings

Identified connections between Fock, vertex, shuffle, and L-operator representations for sl(n).

Extended previous results from gl(1) to sl(n) case.

Provides a unified framework for different realizations of quantum toroidal algebras.

Abstract

In this paper, we relate the well-known Fock representations of the quantum toroidal algebra of sl(n) to the vertex, shuffle, and L-operator representations of the same algebra. These identifications generalize those for the quantum toroidal algebra of gl(1), which were recently established by Feigin-Jimbo-Miwa-Mukhin.