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arXiv · 1602.08457

Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations

Nicolai Reshetikhin·Jasper Stokman·Bart Vlaar
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Abstract

We construct integral representations of solutions to the boundary quantum Knizhnik-Zamolodchikov equations. These are difference equations taking values in tensor products of Verma modules of quantum affine $\mathfrak{sl}_2$, with the K-operators acting diagonally. The integrands in question are products of scalar-valued elliptic weight functions with vector-valued trigonometric weight functions (boundary Bethe vectors). These integrals give rise to a basis of solutions of the boundary qKZ equations over the field of quasi-constant meromorphic functions in weight subspaces of the tensor product.

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Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar. 2016-02-26. Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations. https://doi.org/10.1016/j.aim.2017.10.041

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