  The higher spin Laplace operator has been constructed recently as the
generalization of the Laplacian in higher spin theory. This acts on functions
taking values in arbitrary irreducible representations of the Spin group. In
this paper, we first provide a decomposition of the higher spin Laplace
operator in terms of Rrita-Schwinger operators. With such a decomposition, a
connection between the fundamental solutions for the higher spin Laplace
operator and the fundamental solutions for the Rarita-Schwinger operators is
provided. Further, we show that the two components in this decomposition are
conformally invariant differential operators. An alternative proof for the
conformally invariance property is also pointed out, which can be connected to
Knapp-Stein intertwining operators. Last but not least, we establish a
Borel-Pompeiu type formula for the higher spin Laplace operator. As an
application, we give a Green type integral formula.
