Hermitian generalization of the Rarita-Schwinger operators
Faculty of Sciences. Mathematics and Computer Science
Acta mathematica Sinica. English series. - Berlin
, p. 311-330
University of Antwerp
We introduce two new linear differential operators which are invariant with respect to the unitary group SU(n). They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator partial derivative((z) under bar) and partial derivative(dagger)((z) under bar) and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials.