On the $W$-algebra in the Calegero-Sutherland model using the Exchange operators

Abstract

We study the $W_{\infty }$ algebra in the Calegero-Sutherland model using the exchange operators. The presence of all the sub-algebras of $W_{\infty }$ is shown in this model. A simplified proof for this algebra, in the symmetric ordered basics, is given. It is pointed out that the algebra contains in general, nonlinear terms. Possible connection to the nonlinear $W_{\infty }$ is discussed.

Plain Tex, no figures, 13 pages

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