Journal of Lie Theory 30 (2020), No. 2, 345--360
Copyright Heldermann Verlag 2020
Conformal Covariance for the Powers of the Dirac Operator
Jean-Louis Clerc
Institut Elie Cartan, Université de Lorraine, 54506 Vandoeuvre-lès-Nancy, France
jean-louis.clerc@univ-lorraine.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 Knapp-Stein 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 Knapp-Stein intertwining operators form a family of operators interpolating between the conformal powers of the Dirac operator.
Keywords: Moebius group, Dirac operator, Knapp-Stein intertwining operators, covariant differential operator.
MSC: 22E45; 43A80.
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