## Boundary quantum Knizhnik-Zamolodchikov equations and fusion

Research output: Contribution to journalArticle

### Standard

Boundary quantum Knizhnik-Zamolodchikov equations and fusion. / Reshetikhin, Nicolai; Stokman, Jasper; Vlaar, Bart Hendrik Maarten.

In: Annales Henri Poincare, Vol. 17, No. 1, 01.2016, p. 137–177.

Research output: Contribution to journalArticle

### Harvard

Reshetikhin, N, Stokman, J & Vlaar, BHM 2016, 'Boundary quantum Knizhnik-Zamolodchikov equations and fusion', Annales Henri Poincare, vol. 17, no. 1, pp. 137–177. https://doi.org/10.1007/s00023-014-0395-4

### APA

Reshetikhin, N., Stokman, J., & Vlaar, B. H. M. (2016). Boundary quantum Knizhnik-Zamolodchikov equations and fusion. Annales Henri Poincare, 17(1), 137–177. https://doi.org/10.1007/s00023-014-0395-4

### Vancouver

Reshetikhin N, Stokman J, Vlaar BHM. Boundary quantum Knizhnik-Zamolodchikov equations and fusion. Annales Henri Poincare. 2016 Jan;17(1):137–177. https://doi.org/10.1007/s00023-014-0395-4

### Author

Reshetikhin, Nicolai ; Stokman, Jasper ; Vlaar, Bart Hendrik Maarten. / Boundary quantum Knizhnik-Zamolodchikov equations and fusion. In: Annales Henri Poincare. 2016 ; Vol. 17, No. 1. pp. 137–177.

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title = "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.",
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