  In this paper we study some operators associated to the Rarita-Schwinger
operators. They arise from the difference between the Dirac operator and the
Rarita-Schwinger operators. These operators are called remaining operators.
They are based on the Dirac operator and projection operators $I-P_k.$ The
fundamental solutions of these operators are harmonic polynomials, homogeneous
of degree $k$. First we study the remaining operators and their representation
theory in Euclidean space. Second, we can extend the remaining operators in
Euclidean space to the sphere under the Cayley transformation.
