THE SYMMETRY STRUCTURE OF THE ANTI-SELF-DUAL EINSTEIN HIERARCHY

An important example of a multi-dimensional integrable system is the a nti-self-dual Einstein equations. By studying the symmetries of these equations, a recursion operator is found and the associated hierarchy constructed. Owing to the properties of the recursion operator one may construct a hierarchy of symmetries and find the algebra generated by them in addition, the Lax pair for this hierarchy is constructed. (C) 1995 American Institute of Physics.