Polynomial Solutions For Arbitrary Higher Spin Dirac Operators

Abstract

In a series of recent papers, we have introduced higher spin Dirac operators, which are far-reaching generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe a general procedure to decompose the polynomial kernel spaces for these operators in irreducible summands for the regular action of the spin group. We will do this in an inductive way, making use of twisted higher spin operators.

2000 AMS Subject Classification::

• 15A66
• 30G35
• 22E46

Keywords:

• Higher spin
• Dirac operators
• representation, spin group, Clifford analysis