From vertex operators to Calogero-Sutherland models

The correlation function of the product of N generalized vertex operators satisfies an infinite set of Ward identities, related to a W_∞ algebra, whose extension out of the mass shell gives rise to equations which can be considered as a generalization of the compactified Calogero-Sutherland (CS) Hamiltonians. In particular the wave function of the ground state of the compactified CS model is shown to be given by the value of the product of N vertex operators between the vacuum and an excited state and the Hamiltonian is identified with W₀² generator. The role of the vertex algebra as underlying unifying structure is pointed out.