
Journal of Lie Theory 30 (2020), No. 2, 345360 Copyright Heldermann Verlag 2020 Conformal Covariance for the Powers of the Dirac Operator JeanLouis Clerc Institut Elie Cartan, Université de Lorraine, 54506 VandoeuvrelèsNancy, France jeanlouis.clerc@univlorraine.fr Bent Oersted Matematisk Institut, 8000 Aarhus C, Denmark orsted@imf.au.dk A new proof of the conformal covariance of the powers of the flat Dirac operator is obtained. The proof uses their relation with the KnappStein family of intertwining operators for the spinorial principal series, and relies on finding the residues of this family. We also treat the compact picture, i.e. on the sphere, where certain natural polynomials of the Dirac operator appear. In effect, it is shown that the KnappStein intertwining operators form a family of operators interpolating between the conformal powers of the Dirac operator. Keywords: Moebius group, Dirac operator, KnappStein intertwining operators, covariant differential operator. MSC: 22E45; 43A80. [ Fulltextpdf (152 KB)] for subscribers only. 