LAX PAIRS OF INTEGRABLE EQUATIONS IN 1-LESS-THAN-OR-EQUAL-TO-D-LESS-THAN-OR-EQUAL-TO-3 DIMENSIONS AS REDUCTIONS OF THE LAX PAIR FOR THE SELF-DUAL YANG-MILLS EQUATION

Symmetry reductions of the self-dual Yang-Mills (SDYM) equations yield various systems of differential equations in lower dimensions. We des cribe a general scheme of reduction of the Lax pair for the SDYM equat ions with respect to an arbitrary subgroup of the conformal group. The compatibility of the reduced Lax pair leads to the SDYM equations red uced under the same symmetry group. The scheme is illustrated by three examples.