EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS

Translationally invariant symmetric polynomials as coordinates for N-b ody problems with identical particles are proposed. It is shown that i n those coordinates the Calogero and Sutherland N-body Hamiltonians, a fter appropriate gauge transformations, can be presented as a quadrati c polynomial in the generators of the algebra sl(N) in finite-dimensio nal degenerate representation. The exact solvability of these models f ollows from the existence of the infinite flag of such representation spaces, preserved by the above Hamiltonians. A connection with Jack po lynomials is discussed.