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arXiv · 1404.5492

Boundary quantum Knizhnik-Zamolodchikov equations and fusion

Nicolai Reshetikhin·Jasper Stokman·Bart Vlaar
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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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Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar. 2014-12-19. Boundary quantum Knizhnik-Zamolodchikov equations and fusion. https://doi.org/10.1007/s00023-014-0395-4

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