  Hermitian monogenic functions are the null solutions of two complex Dirac
type operators. The system of these complex Dirac operators is overdetermined
and may be reduced to constraints for the Cauchy datum together with what we
called the Hermitian submonogenic system (see [8],[9]). This last system is no
longer overdetermined and it has properties that are similar to those of the
standard Dirac operator in Euclidean space, such as a Cauchy-Kowalevski
extension theorem and Vekua type solutions. In this paper, we investigate plane
wave solutions of the Hermitian submonogenic system, leading to the
construction of a Cauchy kernel. We also establish a Stokes type formula that,
when applied to the Cauchy kernel provides an integral representation formula
for Hermitian submonogenic functions.
