Boundary scattering in massless $Ad{S}_3$

We study the boundary integrability problem of the massless sector of $Ad{S}_3\times S^3\times T^4$ string theory. Exploiting the difference-form of the massless scattering theory, we find a very simple and exhaustive list of reflection matrices for all the possible boundary coideal subalgebras - singlet and vector representations, right and left boundary - and check basic properties of our solutions, primarily the boundary Yang-Baxter equation, for all possible combinations of scattering particles.