Lax pair formulation of the N=4 Toda chain (KdV) hierarchy in N=4 superspace

Lax pair and Hamiltonian formulations of the N=4 supersymmetric Toda chain (KdV) hierarchy in N=4 superspace are proposed. The general formulae for the infinite tower of its bosonic flows in terms of the Lax operator in N=4 superspace are derived. A new N=4 superfield basis in which the flows are local is constructed and its embedding in the N=4 O(4) superconformal supercurrent is established. A proof that the flows possess five complex conjugations and aninfinite-dimensional group of discrete symmetries in N=4 superspace is presented. A relation between the two descriptions of the hierarchy in N=4 superspace used in the literature is established. All known N=2 superfield representations of the N=4 KdV hierarchy are shown to derive from our N=4 superspace Lax representation.