Boundary transfer matrices and boundary quantum KZ equations

TL;DR

This paper establishes a new connection between boundary transfer matrices and boundary quantum KZ equations in quantum integrable systems, providing fresh insights into their structure and properties.

Contribution

It introduces a simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations, and derives the commutativity of boundary transfer matrices without relying on crossing symmetry or unitarity.

Findings

Boundary quantum KZ equations are motivated by boundary transfer matrices.

Commutativity of boundary transfer matrices is proven without crossing symmetry.

A relation between transfer matrices and boundary quantum KZ equations is established.

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.