Geodesic
Conformal Covariance for the Powers of the Dirac Operator
Journal of Lie theory, Tome 30 (2020) no. 2, pp. 345-36
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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.
Classification : 22E45, 43A80
Mots-clés : Moebius group, Dirac operator, Knapp-Stein intertwining operators, covariant differential operator 
@article{JLT_2020_30_2_JLT_2020_30_2_a3,
     author = {J.-L. Clerc and B. Oersted},
     title = {Conformal {Covariance} for the {Powers} of the {Dirac} {Operator}},
     journal = {Journal of Lie theory},
     pages = {345--36},
     year = {2020},
     volume = {30},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a3/}
}
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J.-L. Clerc; B. Oersted. Conformal Covariance for the Powers of the Dirac Operator. Journal of Lie theory, Tome 30 (2020) no. 2, pp. 345-36. http://geodesic.mathdoc.fr/item/JLT_2020_30_2_JLT_2020_30_2_a3/