Quaternionic-analytic automorphic forms in Yang-Mills theory

With special variants of quaternionic automorphic forms we set up a closed formula for the fundamental solution of the Dirac equation on some conformally flat spin manifolds in R4, for example on the 4-torus, the Hopf manifold S1 x S3 and on k-handled 4-tori. These in turn can be interpreted as self-dual solutions to the Yang-Mills equation for SU(2)-instantons on thesemanifolds. With a special quaternionic argument principle one obtains an explicit link between these solutions and the Chern index of the SU(2)-principal bundles over these manifolds.