INFINITE SYMMETRY OF THE SPIN SYSTEMS WITH INVERSE-SQUARE INTERACTIONS

One-dimensional quantum particle system with SU(nu) spins interacting through inverse square interactions is studied. We reveal algebraic st ructures of the system: hidden symmetry is the U(nu) congruent-to SU(n u) x U(1) current algebra. This is consistent with the fact that the g round state wave function is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, w hich is the w1+infinity algebra. With this W algebra we can clarify si multaneously the structures of the Calogero type (1/x2-interactions) a nd Sutherland type (1/sin2 x-interactions). The Yangian symmetry is br iefly discussed.