Boundary transfer matrices and boundary quantum KZ equations

Abstract

A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin's boundary transfer matrices by merely imposing appropriate reflection equations, i.e. without using the conditions of crossing symmetry and unitarity of the R-matrix.

26 pages; 2 figures; strengthening of results in Section 2; small modifications (corrected typos etc.) throughout; updated Acknowledgments

References in corpus (3)

• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices
• Boundary quantum Knizhnik-Zamolodchikov equations and fusion

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• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations
• Shor-Movassagh chain leads to unusual integrable model
• Tensor K-matrices for quantum symmetric pairs
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations
• Boundary transfer matrices arising from quantum symmetric pairs
• Triangular solutions to the reflection equation for $U_q(\widehat{s{l}_n})$