Free Boson Representation of $D{Y}_{\hslash }(s{l}_2{)}_k$ and the Deformation of the Feigin-Fuchs

Abstract

A realization of the Yangian double with center $D{Y}_{\hslash }(s{l}_2{)}_k$ of level $k(\ne 0,-2)$ in terms of free boson fields is constructed. The screening currents are also presented, which commute with $D{Y}_{\hslash }(s{l}_2)$ modulo total difference. In the $\hslash \to 0$ limit, the currents of Yangian double $D{Y}_{\hslash }(s{l}_2{)}_k$ becomes the Feigin-Fuchs realization of affine Lie $sl(2{)}_k$, while the screening currents of Yangian double $D{Y}_{\hslash }(s{l}_2{)}_k$ becomes the screening currents of the affine Lie algebra $sl(2{)}_k$.

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