REDUCTIONS OF A LAX PAIR FOR SELF-DUALITY EQUATIONS OF THE YANG-MILLSMODEL

Reductions of the self-duality equation of the Yang-Mills model in d=4 in terms of the action of continuous symmetry groups lead to systems of differential equations in a lower dimensionality. An algorithm is w ritten for reducing a Lax pair for self-duality equations with respect to an arbitrary subgroup of the conformal transformation group of R4 space. The compatibility condition for the reduced Lax pair is shown t o be the same as the self-duality equations reduced in terms of the ac tion of the same symmetry group. The general scheme is illustrated wit h three examples.