Abstract
We study the boundary integrability problem of the massless sector of AdS₃ × S³ × T⁴ string theory. We obtain the massless 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 in all possible combinations of scattering particles. We exploit the difference-form of the massless scattering theory to find a very simple and exhaustive list of reflection matrices. *