Annales Henri Poincaré

, Volume 17, Issue 1, pp 137–177 | Cite as

Boundary Quantum Knizhnik–Zamolodchikov Equations and Fusion

  • Nicolai Reshetikhin
  • Jasper Stokman
  • Bart Vlaar


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.


Linear Operator Tensor Product Spin Chain Evaluation Representation Verma Module 
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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Nicolai Reshetikhin
    • 1
    • 2
    • 3
  • Jasper Stokman
    • 2
    • 4
  • Bart Vlaar
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.KdV Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.ITMO UniversitySaint PetersburgRussia
  4. 4.IMAPPRadboud UniversityNijmegenThe Netherlands

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