On the W-algebra in the Calogero-Sutherland model using exchange operators

Abstract

We study the W∞-algebra in the Calogero-Sutherland model using the exchange operators. The presence of all the subalgebras of W∞ is shown in this model. A simplified proof for this algebra, in the symmetric ordered basis, is given. It is pointed out that the algebra contains in general, nonlinear terms. This shows that the ordinary W∞-algebra is not present in this model. Possibility of the presence of the nonlinear W∞-algebra is discussed.