k-Dirac operator and the Cartan-Kahler theorem

Abstract

We apply the Cartan-Kähler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for k=2 the tableaux of the first prolongations of these two operators are involutive.

This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.

Keywords

• k-Dirac
• operator
• Cartan-Kahler
• theorem