  This paper demonstrates the power of the calculus developed in the two
previous parts of the series for all real forms of the almost Hermitian
symmetric structures on smooth manifolds, including e.g. conformal Riemannian
and almost quaternionic geometries. Exploiting some finite dimensional
representation theory of simple Lie algebras, we give explicit formulae for
distinguished invariant curved analogues of the standard operators in terms of
the linear connections belonging to the structures in question, so in
particular we prove their existence. Moreover, we prove that these formulae for
k-th order standard operators, k=1,2,..., are universal for all geometries in
question.
