A Q-Operator for Open Spin Chains II: Boundary Factorization

Abstract

One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underlying this is a factorization formula for L-operators (solutions of the Yang-Baxter equation associated to particular infinite-dimensional representations). To extend such a formalism to open spin chains, one needs a factorization identity for solutions of the reflection equation (boundary Yang-Baxter equation) associated to these representations. In the case of quantum affine ${\mathrm{sl}}_2$ and diagonal K-matrices, we derive such an identity using the recently formulated theory of universal K-matrices for quantum affine algebras.