SYMMETRIES OF THE ABLOWITZ-KAUP-NEWELL-SEGUR HIERARCHY

Nonlocal symmetries of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy are introduced and it is shown that the symmetry algebra of the AKNS hierarchy is isomorphic to the loop algebra sl(2,C) x C[lambda,lambda( -1)]. As a special case, the symmetry algebra of the nonlinear Schrodi nger equation is determined and is shown to be isomorphic to the loop algebra su(2) x R[lambda,lambda(-1)] or g x R[lambda,lambda (-1)] corr esponding to the sign of the nonlinear term, where g is a noncompact r eal form of sl(2,C).