COLLECTIVE FIELD-THEORY, CALOGERO-SUTHERLAND MODEL AND GENERALIZED MATRIX MODELS

On the basis of the collective field method, we analyze the Calogero-S utherland model (CSM) and the Selberg-Aomoto integral, which defines, in particular case, the partition function of the matrix models. Verte x operator realizations for some of the eigenstates (the Jack polynomi als) of the CSM Hamiltonian are obtained. We derive Virasoro constrain t for the generalized matrix models and indicate relations with the CS M operators. Similar results are presented for the q-deformed case (th e Macdonald operator and polynomials), which gives the generating func tional of infinitely many conserved charges in the CSM.