Infinite Symmetry of the Spin Systems with Inverse Square Interactions

One-dimensional quantum particle system with SU(v) spins interacting through inverse square interactions is studied. We reveal algebraic structures of the system: hidden symmetry is the U (v) = SU(v)⊗U(1) current algebra. This is consistent with the fact that the ground state wave function is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, which is the Wi+∞ algebra. With this W algebra we can clarify simultaneously the structures of the Calogero type (1/x2-interactions) and Sutherland type (1/sin2 x-interactions). The Yangian symmetry is briefly discussed.