Free Boson Representation of $U_q(\widehat{sl}_3)$

TL;DR

This paper constructs a free boson representation of the quantum affine algebra $U_q(\\widehat{sl}_3)$ at arbitrary level, extending Wakimoto's approach and deriving screening currents that commute with the algebra's action.

Contribution

It provides a new free boson realization of $U_q(\widehat{sl}_3)$ for any level, generalizing the Wakimoto representation to the quantum case.

Findings

Constructed a bosonic realization of $U_q(\widehat{sl}_3)$

Derived screening currents that commute with the algebra

Reduces to Wakimoto representation as $q \to 1$

Abstract

A representation of the quantum affine algebra $U_{q}(\widehat{sl}_3)$ of an arbitrary level $k$ is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in the $q \rightarrow 1$ limit. The analogues of the screening currents are also obtained. They commute with the action of $U_{q}(\widehat{sl}_3)$ modulo total differences of some fields.