Abstract. A procedure to construct K-matrices from the generalized q-Onsager algebra Oq( g) 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 Oq(a (2) 2 ) and Oq(a 2 ) are treated in details.

Abstract:We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in particular with the so-called dressing phase problem.We also show how the models can be interpreted, in condensed matter physics, as integrable multi-leg Hubbard models.

We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m) ⊕ gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase due to the integration of a subset of 'simple' Bethe equations. We discuss relations with AdS/CFT correspondence, and with condensed matter physics.