We propose explicit expressions for the boundary reflection matrices of the \({\mathcal{A}}_{m}+(r, s)\) series of massive scattering theories, obtained by perturbing the \({\mathcal{A}}_{m}\) unitary minimal models with (r, s) boundary conditions with both bulk and boundary ϕ1,3 operators. We identify the vacua that live on the boundary with the allowed edges of the (r, s) conformal boundary conditions of the Am Andrews-Baxter-Forrester model. The boundary reflection matrices are then “direct sums” of certain pairs of Am−1 Behrend-Pearce solutions of the boundary Yang-Baxter equation and are consistent with the boundary bootstrap and the recently-introduced crossing, as well as the Z2 (height-reversal), Kac table and non-invertible symmetries.
