For the integrable long-range SU( M ) spin chain, the exact ground-state wave function is constructed for arbitrary irreducible representation of the permutation group.
Excitation spectra in the SU(ν+1,1) supersymmetric t-J model with long-range exchange and transfer has quadratic dependence on spin and charge currents for all energies. After brief review on the supersymmetry, this paper gives a simple explanation for the spin-charge separation on the basis of a first-quantized representation. A useful identity is derived on permutation properties of SU(ν) Jastrow-type wave functions, which constitute the ground states for a class of 1/r2 interaction models.