  We construct generalizations of the Calogero-Sutherland-Moser system by
appropriately reducing a model involving many unitary matrices. The resulting
systems consist of particles on the circle with internal degrees of freedom,
coupled through modifications of the inverse-square potential. The coupling
involves SU(M) non-invariant (anti)ferromagnetic interactions of the internal
degrees of freedom. The systems are shown to be integrable and the spectrum and
wavefunctions of the quantum version are derived.
