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The reduction by symmetry of the linear system of the self-dual Yang-Millsequations in four-dimensions under representatives of the conjugacy classes ofsubgroups of the connected part to the identity of the corresponding Euclideangroup under itself is carried out. Only subgroups leading to systems ofdifferential equations nonequivalent to conditions of zero curvature withoutparameter, or to systems of uncoupled first order linear O.D.E.'s areconsidered. Lax pairs for a modified form of the Nahm's equations as well asfor systems of partial differential equations in two and three dimensions arewritten out.Comment: 27 pages, LaTeX209 fil

Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations