Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations

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.

35 pages, 1 figure

References in corpus (1)

• Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations

Cited by in corpus (3)

• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
• Tensor K-matrices for quantum symmetric pairs
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations