CONSTRUCTION OF KP HIERARCHIES IN TERMS OF FINITE NUMBER OF FIELDS AND THEIR ABELIANIZATION

The 2M-boson representations of the KP hierarchy are constructed in terms of M mutually independent two-boson KP representations for arbitrary number M. Our construction establishes the multi-boson representations of the KP hierarchy as consistent Poisson reductions of the standard KP hierarchy within the R-matrix scheme. As a byproduct we obtain a complete description of any finitely-many-field formulation of the KP hierarchy in terms of Darboux coordinates with respect to the first Hamiltonian structure. This results in a series of representations of W1+infinity algebra made out of an arbitrary even number of boson fields.