EXPLICIT SOLUTION OF THE QUANTUM 3-BODY CALOGERO-SUTHERLAND MODEL

The class of quantum integrable systems associated with root systems w as introduced by Olshanetsky and Perelomov as a generalization of the Calogero-Sutherland systems. It was recently shown by one of the autho rs that for such systems with a potential upsilon(q) = kappa(kappa - 1 ) sin(-2) q, the series in the product of two wavefunctions is the K-d eformation of the Clebsch-Gordan series. This yields recursion relatio ns for the wavefunctions of those systems and, related to them, for ge neralized zonal spherical functions on symmetric spaces.In this letter this approach is used to compute the explicit expressions for the thr ee-body Calogero-Sutherland wavefunctions, which are the Jack polynomi als. We conjecture that similar results are also valid for the more ge neral two-parameters deformation ((q,t)-deformation) introduced by Mac donald.