  By using the self-dual Yang-Mills (SDYM) equation as an example, we study a
method for relating symmetries and recursion operators of two partial
differential equations connected to each other by a non-auto-Backlund
transformation. We prove the Lie-algebra isomorphism between the symmetries of
the SDYM equation and those of the potential SDYM (PSDYM) equation, and we
describe the construction of the recursion operators for these two systems.
Using certain known aspects of the PSDYM symmetry algebra, we draw conclusions
regarding the Lie algebraic structure of the "potential symmetries" of the SDYM
equation.
