Deformed oscillators algebra formulation of the Nonlinear Schrödinger hierarchy and of its symmetry

We present a self-contained formulation of the Nonlinear Schrödinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y (glN ) and finite W (glpN , N.glp) algebras is also illustrated in this framework. To be published in the proceedings of QGIS-99, Prague, June 17-19 1999 July 1999 LAPTH-743/99-Conf hep-th/9907218 [email protected] The present text is a summary of the original work [1], done in collaboration with M. Mintchev, P. Sorba and Ph. Zaugg. The proofs and detailed calculations can be found there, as well as a more precise bibliography.