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

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 written 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 to be the same as the self-duality equations reduced in terms of the action of the same symmetry group. The general scheme is illustrated with three examples.