Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry

A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where R-matrix solutions of the Yang-Baxter equation do not have the property of crossing unitarity. Suitably modified forms of the reflection equations are presented which permit the construction of a family of commuting transfer matrices. As an example, we apply the formalism to determine the most general solutions of the reflection equations for a solution of the Yang-Baxter equation with underlying symmetry given by the Drinfeld double D(D3) of the dihedral group D3. This R-matrix does not have the crossing unitarity property. In this manner we derive integrable boundary conditions for an open chain model of interacting non-Abelian anyons.