The elliptic quantum algebra Uq,ₚ(slₙ) and its vertex operators

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