Integrability, fusion, and duality in the elliptic Ruijsenaars model

The generalized elliptic Ruijsenaars models, which are regarded as a difference analog of the Calogero-Sutherland-Moser models associated with the classical root systems are studied. The integrability and the duality using the fusion procedure of operator-valued solutions of the Yang-Baxter equation and the reflection equation are shown. In particular a new integrable difference operator of type-D is proposed. The trigonometric models are also considered in terms of the representation of the affine Hecke algebra.