N=2 local and N=4 non-local reductions of supersymmetric KP hierarchy in N=2 superspace

An N = 4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are de scribed, This class includes the one-dimensional reduction of the two-dimen sional N = (2\2) superconformal Toda lattice hierarchy possessing the N = 4 supersymmetry - the N = 4 Toda chain hierarchy - which may be relevant in the construction of supersymmetric matrix models. The Lax-pair representati ons of the bosonic and fermionic flows, corresponding local and non-local H amiltonians, finite and infinite discrete symmetries, the first two Hamilto nian structures and the recursion operator connecting all evolution equatio ns and the Hamiltonian structures of the N = 4 Toda chain hierarchy are con structed in explicit form, Its secondary reduction to the N = 2 supersymmet ric alpha = - 2 KdV hierarchy is discussed. (C) 1999 Published by Elsevier Science B.V. All rights reserved.