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