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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
Article

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.

Keywords

Linear Operator Tensor Product Spin Chain Evaluation Representation Verma Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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