Vertex Operators and Matrix Elements of Uq(su(2)ₖ) via Bosonization

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We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of Uq(su(2)ₖ) for arbitrary level k and representation j≤ k/2. Both are obtained directly as two solutions of the defining condition of vertex operators - namely that they intertwine Uq(su(2)ₖ) modules. We construct the screening charge and present a formula for the n-point function. Specializing to j=1/2 we construct all VOs and CVOs explicitly. The existence of the CVO allows us to place the calculation of the two-point function on the same footing as k=1; that is, it is obtained without screening currents and involves only a single integral from the CVO. This integral is evaluated and the resulting function is shown to obey the q-KZ equation and to reduce simply to both the expected k=1 and q=1 limits.