Dunkl Operators and Calogero-Sutherland Models

We describe a general method for constructing (scalar or spin) Calogero-Sutherland models of A_N or BC_N type, which are either exactly or quasi-exactly solvable. Our approach is based on the simultaneous use of three different families of Dunkl operators of each type, one of which was recently introduced by the authors. We perform a complete classification of the models which can be constructed by our method. We obtain in this way several new families of (quasi-)exactly solvable Calogero-Sutherland models, some of them with elliptic interactions.