  A new proof of the conformal covariance of the powers of the flat Dirac
operator is obtained. The proof uses their relation with the Knapp-Stein
intertwining operators for the spinorial principal series. We also treat the
compact picture, i.e. the corresponding operators on the sphere, where certain
polynomials of the Dirac operator appear. This gives a new
representation-theoretic framework for earlier results.
