THE N=2 SUPERSYMMETRIC TODA LATTICE HIERARCHY

We propose a new integrable N = 2 supersymmetric Toda lattice hierarch y which may be relevant for constructing a supersymmetric one-matrix m odel. We define its first two Hamiltonian structures, the recursion op erator and Lax-pair representation. We provide partial evidence for th e existence of an infinite-dimensional N = 2 superalgebra of its flows . We study its bosonic limit and introduce new Lax-pair representation s for the bosonic Toda lattice hierarchy. Finally we discuss the relev ance this approach for constructing N = 2 supersymmetric generalized T oda lattice hierarchies. (C) 1998 Elsevier Science B.V.