The elliptic quantum algebra $U_{q,p}(\widehat{s{l}_N})$ and its vertex operators

Abstract

We construct a realization of the elliptic quantum algebra $U_{q,p}(\widehat{s{l}_N})$ for any given level $k$ in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization of the quantum affine algebra $U_q(\widehat{s{l}_N})$. We also construct a family of screening currents, which commute with the currents of $U_{q,p}(\widehat{s{l}_N})$ up to total q-differences. And we give explicit twisted expressions for the type $I$ and the type $II$ vertex operators of $U_{q,p}(\widehat{s{l}_N})$ by twisting the known results of the type $I$ vertex operators of the quantum affine algebra $U_q(\widehat{s{l}_N})$ and the new results of the type $II$ vertex operators of $U_q(\widehat{s{l}_N})$ we obtained in this paper.

28 pages

References in corpus (2)

• On explicit free field realizations of current algebras
• On the Vertex Operators of the Elliptic Quantum Algebra $U_{q,p}(\widehat{s{l}_2}{)}_k$}