INTEGRABILITY, FUSION, AND DUALITY IN THE ELLIPTIC RUIJSENAARS MODEL

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