A toy model for higher spin Dirac operators

This paper deals with the higher spin Dirac operator Q_2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight $ (tfrac{5} {2},tfrac{3} {2},tfrac{1} {2},...,tfrac{1} {2}) $ (tfrac{5} {2},tfrac{3} {2},tfrac{1} {2},...,tfrac{1} {2}) . This operator acts as a toy model for generalizations of the classical Rarita—Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.