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

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. 1 Email: [email protected] 2 Email: [email protected]