K. Hikami et M. Wadati, INTEGRABLE SYSTEMS WITH LONG-RANGE INTERACTIONS, W-INFINITY ALGEBRA, AND ENERGY-SPECTRUM, Physical review letters, 73(9), 1994, pp. 1191-1194
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.