On The Hamiltonian Structures and The Reductions of The KP Hierarchy

Recent work on a free field realization of the Hamiltonian structures of the classical KP hierarchy and of its flows is reviewed. It is shown that it corresponds to a reduction of KP to the NLS system. (Talk given by D.A.D. at the NSERC-CAP Workshop on Quantum Groups, Integrable Models and Statistical Systems, Kingston, Canada July 13-17 1992.)