Boundary Quantum Knizhnik-Zamolodchikov Equations and Fusion

In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov (qKZ) equations with diagonal K-operators to higher spin representations of quantum affine sl2. First we give a systematic exposition of known results on R-operators acting in the tensor product of evaluation representations in Verma modules over quantum sl2. We develop the corresponding fusion of K-operators, which we use to construct diagonal K-operators in these representations. We construct Jackson integral solutions of the associated boundary qKZ equations and explain how in the finite-dimensional case they can be obtained from our previous results by the fusion procedure.