The elliptic quantum algebra U_{q\\scriptsize,\, p}(\widehat{sl_N}) and its vertex operators

We construct a realization of the elliptic quantum algebra U_{q,p}(\widehat{sl_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{sl_N}) . We also construct a family of screening currents, which commute with the currents of U_{q,p}(\widehat{sl_N}) up to total q-differences. And we give explicit twisted expressions for the type I and type II vertex operators of U_{q,p}(\widehat{sl_N}) by twisting the known results of the type I vertex operators of the quantum affine algebra U_{q}(\widehat{sl_N}) and the new results of the type II vertex operators of U_{q}(\widehat{sl_N}) we obtained in this paper.