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Hermitian monogenic functions are the null solutions of two complex Diractype operators. The system of these complex Dirac operators is overdeterminedand may be reduced to constraints for the Cauchy datum together with what wecalled the Hermitian submonogenic system (see [8],[9]). This last system is nolonger overdetermined and it has properties that are similar to those of thestandard Dirac operator in Euclidean space, such as a Cauchy-Kowalevskiextension theorem and Vekua type solutions. In this paper, we investigate planewave solutions of the Hermitian submonogenic system, leading to theconstruction of a Cauchy kernel. We also establish a Stokes type formula that,when applied to the Cauchy kernel provides an integral representation formulafor Hermitian submonogenic functions.

A Cauchy kernel for the Hermitian submonogenic system