Generalized q-Onsager algebras and dynamical K-matrices

A procedure to construct K-matrices from the generalized q-Onsager algebra O-q((g) over bar) is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to dynamical (non-c-number) solutions. It shows the relation between soliton non-preserving reflection equations or twisted reflection equations and the generalized q-Onsager algebras. These dynamical K-matrices are important to quantum integrable models with extra degrees of freedom located at the boundaries; for instance, in the quantum affine Toda field theories on the half-line, they yield the boundary amplitudes. As examples, the cases of O-q(a(2)((2))) and O-q(a(2)((1))) are treated in detail.