Iterated Dirac Operators in ${\mathbb{C}}^n$

Abstract

We give a clssification of linear, conformally invariant, Clifford algebra valued differential operators over ${\mathbb{C}}^n$. Such operators comprise of the Dirac operator and its iterates. We show that the function theory, associated to the Dirac operator in ${\mathbb{R}}^n$ and ${\mathbb{C}}^n$ can be generalized to all these operators.