Abstract
A condition on the self-duality and the stability of Yang-Mills solutions are discussed. The canonical invariant G G -connections on S 4 {S^4} and P 2 ( C ) {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 G G -vector bundles ( G G is a compact simple group). Under a certain property of the isotropy homomorphism, these canonical connections are not weakly stable.
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