  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 have 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 $\mathfrak{sl}_2$ and diagonal K-matrices, we
derive such an identity using the recently formulated theory of universal
K-matrices for quantum affine algebras.
