U q [sl (2| ∧ 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Abstract

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra Uq[sl(2|∧1)] are constructed for arbitrary level k=α, where α≠0,−1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-α highest weight Fock–Wakimoto modules. Screen currents which commute with the action of Uq[sl(2|∧1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed.