Quasi-Exact Solvability And Calogero-Sutherland Models

We introduce a new family of Dunkl operators preserving a polynomial subspace of finite dimension. Several new quantum Calogero–Sutherland models are then obtained by generalizing the methods of one-dimensional QES theory. These models describe many particles with or without spin moving in one spatial dimension. A complete classification has been performed, which shows the first examples of models with elliptic interaction for which some eigenvalues can be calculated in an explicit way.