MULTIFIELD REPRESENTATIONS OF THE KP HIERARCHY AND MULTIMATRIX MODELS

We discuss the integrable hierarchies that appear in multi-matrix mode ls. They can be envisaged as multi-field representations of the KP hie rarchy. We then study the possible reductions of this systems via the Dirac reduction method by suppressing successively one by one part of the fields. We find in this way new integrable hierarchies, of which w e are able to write the Lax pair representations by means of suitable Drinfeld-Sokolov linear systems. At the bottom of each reduction proce dure we find an Nth KdV hierarchy. We discuss in detail the case which leads to the KdV hierarchy and to the Boussinesque hierarchy, as well as the general case in the dispersionless limit.