N-point matrix elements of dynamical vertex operators of the higher spin XXZ model

We extend the concept of conjugate vertex operators, first introduced by Dotsenko in the case of the bosonization of the $su(2)$ conformal field theory, to the bosonization of the dynamical vertex operators (type II in the classification of the Kyoto school) of the higher spin XXZ model. We show that the introduction of the conjugate vertex operators leads to simpler expressions for the N-point matrix elements of the dynamical vertex operators, that is, without redundant Jackson integrals that arise from the insertion of screening charges. In particular, the two-point matrix element can be represented without any integral.