Rarita-Schwinger type operators in Clifford analysis

In this paper we investigate a generalization of the classical Rarita-Schwi nger equations for spin 3/2 fields to the case of functions taking values i n irreducible representation spaces with weight k+1/2. These fields may be realised as functions taking values in spaces of spherical monogenics earli er considered in F. Sommen and N. Van Acker (1993, in "Clifford Algebras an d Their Applications in Mathematical Physics." Kluwer Academic, Dordrecht / Norwell, MA). In this paper we develop the main function theoretic results . (C) 2001 Academic Press.