INTEGRABLE SYSTEMS WITH LONG-RANGE INTERACTIONS, W-INFINITY ALGEBRA, AND ENERGY-SPECTRUM

Quantum integrable particle systems with inverse square interactions i n one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with SU(nu) spins, a hid den symmetry is the SU(nu) x U(1) congruent-to U(nu) current algebra. The system has a higher symmetry, the W1+infinity algebra. This W alge bra structure unifies the Calogero type (1/x2 interactions) and the Su therland type (1/sin2 x interactions). The energy spectra of the syste ms are obtained in a simple manner based on the fermion representation of the algebra.