INTEGRABLE 3-BODY PROBLEMS WITH 2-BODY AND 3-BODY INTERACTIONS

Spin generalizations of both the elliptic Calogero-Marchioro-WoIfes mo del and the nonlinear Schrodinger model are studied. These models are three-body problems with two- and three-body potentials, and mathemati cally related with the exceptional root system of type G(2). We constr uct the integrable differential-difference operator, the so-called Dun kl operator, based on the infinite-dimensional representation for solu tions of the variant of the classical Yang-Baxter equation. By use of these operators, we investigate the integrability and the scattering m atrices.