SYMMETRIES, CURRENTS AND CONSERVATION-LAWS OF SELF-DUAL GRAVITY

We describe an infinite-dimensional algebra of hidden symmetries for t he self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w(infinity) algebra),this algebra cont ains new hidden symmetries, which are an affine extension of the Loren tz rotations. The full symmetry algebra has both Kac-Moody and Virasor o-like generators, whose exponentiation maps solutions of the field eq uations to other solutions. Relations to problems of string theories a re briefly discussed.