Infinite Symmetry of the One-Dimensional System with Inverse Square Interactions

Abstract

We consider the one-dimensional quantum particle system with inverse square interactions, and reveal the underlying infinite symmetry. We construct explicitly the W-operators to show that the system represents the w_<1+∞>-algebra. Both the Calogero-type (1/x^2-interactions) and Sutherland-type (1/sin^2x-interactions) models are included in these operators : the former is the spin-1 operators and the latter the zero-mode operators. The symmetry of the Calogero-Moser-type (Calogero-type model confined in the harmonic potential) is also discussed.