The ADHM Construction and Non-local Symmetries of the Self-dual Yang-Mills Equations

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang -Mills equations on R(4) discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-instanton moduli space. This action simply corresponds to a scaling of the moduli space.