The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3300–3311 | Cite as

Conformally Covariant Differential Operators for the Diagonal Action of \(O(p,\,q)\) on Real Quadrics

  • Jean-Louis ClercEmail author


Let \(X=G/P\) be a real projective quadric, where \(G=O(p,\,q)\) and P is a parabolic subgroup of G. Let \((\pi _{\lambda ,\epsilon },\, \mathcal H_{\lambda ,\epsilon })_{ (\lambda ,\epsilon )\in {\mathbb {C}}\times \{\pm \}}\) be the family of (smooth) representations of G induced from the characters of P. For \((\lambda ,\, \epsilon ),\, (\mu ,\, \eta )\in {\mathbb {C}}\times \{\pm \},\) a differential operator \(\mathbf D_{(\mu ,\eta )}^\mathrm{reg}\) on \(X\times X,\) acting G-covariantly from \({\mathcal {H}}_{\lambda ,\epsilon } \otimes {\mathcal {H}}_{\mu , \eta }\) into \({\mathcal {H}}_{\lambda +1,-\epsilon } \otimes {\mathcal {H}}_{\mu +1, -\eta }\) is constructed.


Conformally covariant differential operator Projective quadric 

Mathematics Subject Classification

43A85 58J70 


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Copyright information

© Mathematica Josephina, Inc. 2017

Authors and Affiliations

  1. 1.Institut Élie CartanUniversité de LorraineVandœuvre-lès NancyFrance

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