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A 3-dimensional reduction of the seld-dual Yang-Mills (SDYM) equation, namedSDYM3, is examined from the point of view of its symmetry and integrabilitycharacteristics. By using a non-auto-Backlund transformation, this equation isconnected to its potential form (PSDYM3) and a certain isomorphism between theLie algebras of symmetries of the two systems is shown to exist. Thisisomorphism allows us to study the infinite-dimensional Lie algebraic structureof the "potential symmetries" of SDYM3 by examining the symmetry structure ofPSDYM3 (which is an easier task). By using techniques described in a recentpaper, the recursion operators for both SDYM3 and PSDYM3 are derived. Moreover,a Lax pair and an infinite set of nonlocal conservation laws for SDYM3 arefound, reflecting the fact that SDYM3 is a totally integrable system. Thissystem may physically represent gravitational fields or chiral fields.

Symmetry and Integrability of a Reduced, 3-Dimensional Self-Dual Gauge Field Model