K. Hikami et M. Wadati, INFINITE SYMMETRY OF THE SPIN SYSTEMS WITH INVERSE-SQUARE INTERACTIONS, Journal of the Physical Society of Japan, 62(12), 1993, pp. 4203-4217
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.