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.
1
Institut Elie Cartan, Université de Lorraine, 54506 Vandoeuvre-lès-Nancy, France
2
Matematisk Institut, 8000 Aarhus C, Denmark
Jean-Louis Clerc; Bent Oersted. Conformal Covariance for the Powers of the Dirac Operator. Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 345-360. http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a3/
@article{JOLT_2020_30_2_a3,
author = {Jean-Louis Clerc and Bent Oersted},
title = {Conformal {Covariance} for the {Powers} of the {Dirac} {Operator}},
journal = {Journal of Lie Theory},
pages = {345--360},
year = {2020},
volume = {30},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a3/}
}
TY - JOUR
AU - Jean-Louis Clerc
AU - Bent Oersted
TI - Conformal Covariance for the Powers of the Dirac Operator
JO - Journal of Lie Theory
PY - 2020
SP - 345
EP - 360
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a3/
ID - JOLT_2020_30_2_a3
ER -
%0 Journal Article
%A Jean-Louis Clerc
%A Bent Oersted
%T Conformal Covariance for the Powers of the Dirac Operator
%J Journal of Lie Theory
%D 2020
%P 345-360
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a3/
%F JOLT_2020_30_2_a3
