Self-duality conditions satisfied by the spin connections of spheres

The spinor connections in the half-spin bundles over S4 are ± self-dual solutions of the Yang-Mills equations of smallest nontrivial Pontrjagin number. When expressed in coordinates they give the original BPST instanton on R4. The purpose of the lecture is to discuss this problem in a more general setting on S4n and obtain in coordinate free way the BPST solution for n=1 and the GKS solution for n=2. 9 refs