Free Boson Representation of $U_{q}(\hat{sl_{2}})$

Abstract

A representation of the quantum affine algebra $U_{q}(\hat{sl_{2}})$ of an arbitrary level $k$ is realized in terms of three boson fields, whose $q \rightarrow 1$ limit becomes the Wakimoto representation. An analogue of the screening current is also obtained. It commutes with the action of $U_{q}(\hat{sl_{2}})$ modulo total difference of some fields.