The Yangian Deformation of the W-Algebras and and the Calogero-Sutherland model

Abstract

The Yangian symmetry Y(su($n$)) of the Calogero-Sutherland-Moser spin model is reconsidered. The Yangian generators are constructed from two non-commuting su($n$)-loop algebras. The latters generate an infinite dimensional symmetry algebra which is a deformation of the $W_{\infty }$-algebra. We show that this deformed $W_{\infty }$-algebra contains an infinite number of Yangian subalgebras with different deformation parameters.

8 pages, latex, 1 figure, to appear in the Proceeding of 6-th Nankai Workshop