Boundary quantum Knizhnik-Zamolodchikov equations and fusion

Abstract

In this paper we extend our previous results concerning Jackson integral solutions of the boundary quantum Knizhnik-Zamolodchikov 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 quantum Knizhnik-Zamolodchikov equations and explain how in the finite-dimensional case they can be obtained from our previous results by the fusion procedure.

36 pages; some small additions and corrections concerning mero-uniform convergence (Defn. 6.1) and rectified some notation issues for the function \mathcal{Y} (p21 and onwards). appears in Annales Henri Poincaré, 2014

References in corpus (4)

• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• On the boundary form factor program
• On universal solution to reflection equation
• Solitons, Boundaries, and Quantum Affine Algebras

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