Orbit and layer structure of complexified SU(4) algebra

We refer to the extension of perturbation theory to a special class of operator-valued functions of a (complex) vector argument, depending on this argument in a covariant way. The semisimplicity of sl(4,C) assures that there is only a finite number of strata and we are able to write explicitly their representatives, stabilizers, dimensions and the corresponding relations in a complete set of invariants. Finally we identify the singular orbits and obtain the behaviour of every smooth invariant function (with respect to the adjoint action). (author)