2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27049Excitation 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/$r^2$ interaction models.8 pages (LaTex)Condensed Mattertext