Decomposition of the twisted Dirac operator

The classical Dirac operator is a conformally invariant first order differential operator mapping spinor-valued functions to the same space, where the spinor space is to be interpreted as an irreducible representation of the spin group. In this article we twist the Dirac operator by replacing the spinor space with an arbitrary irreducible representation of the spin group. In this way, the operator becomes highly reducible, whence we determine its full decomposition