Conformal covariance for the powers of the Dirac operator

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.