# $k$-Dirac operator and the Cartan-Kähler theorem

## Tomáš Salač

Address: Faculty of Mathematics and Physics, Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic

E-mail: salac@karlin.mff.cuni.cz

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.

AMSclassification: primary 11A11.

Keywords: .

DOI: 10.5817/AM2013-5-333