Abstract
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 \({\mathfrak{sl}_2}\). 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 \({\mathfrak{sl}_2}\). 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.
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Communicated by Claude Alain Pillet
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Reshetikhin, N., Stokman, J. & Vlaar, B. Boundary Quantum Knizhnik–Zamolodchikov Equations and Fusion. Ann. Henri Poincaré 17, 137–177 (2016). https://doi.org/10.1007/s00023-014-0395-4
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DOI: https://doi.org/10.1007/s00023-014-0395-4