Invariant Connections and Yang-Mills Solutions

A condition on the self-duality and the stability of Yang-Mills solutions are discussed. The canonical invariant -connections on and <!-- MATH ${P_2}({\mathbf{C}})$ --> are considered as Yang-Mills solutions. The non-self-duality of the connections requires the injectivity of the isotropy homomorphisms. We construct examples of non-self-dual connections on -vector bundles ( is a compact simple group). Under a certain property of the isotropy homomorphism, these canonical connections are not weakly stable.