Comptes Rendus
no. 7
Group theory/Differential geometry
Classification of differential symmetry breaking operators for differential forms
[Classification des opérateurs de brisure de symétrie pour les formes différentielles]

Présenté par : Michel Duflo

Toshiyuki Kobayashi1 ; Toshihisa Kubo2 ; Michael Pevzner3
1 Kavli IPMU and Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
2 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
3 Laboratoire de Mathématiques, Université de Reims-Champagne-Ardenne, CNRS FR 3399, 51687 Reims, France
Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 671-676.

Nous présentons une classification complète des opérateurs différentiels conformément covariants agissant entre les espaces des i-formes différentielles sur la sphère Sn et ceux des j-formes sur la hypershère totalement géodésique Sn−1 en analysant les restrictions des représentations des séries principales du groupe de Lie O(n+1,1). Pour de tels opórateurs à valeurs matricielles, nous donnons des formules explicites dans les coordonnées plates et trouvons des identités de factorisation.

We give a complete classification of conformally covariant differential operators between the spaces of differential i-forms on the sphere Sn and j-forms on the totally geodesic hypersphere Sn−1 by analyzing the restriction of principal series representations of the Lie group O(n+1,1). Further, we provide explicit formulæ for these matrix-valued operators in the flat coordinates and find factorization identities for them.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.04.012
Toshiyuki Kobayashi 1 ; Toshihisa Kubo 2 ; Michael Pevzner 3

1 Kavli IPMU and Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
2 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan
3 Laboratoire de Mathématiques, Université de Reims-Champagne-Ardenne, CNRS FR 3399, 51687 Reims, France 
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Toshiyuki Kobayashi; Toshihisa Kubo; Michael Pevzner. Classification of differential symmetry breaking operators for differential forms. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 671-676. doi : 10.1016/j.crma.2016.04.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.012/

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Cité par Sources :

☆ The first named author was partially supported by Institut des Hautes Études Scientifiques, France and Grant-in-Aid for Scientific Research (A) (25247006), Japan Society for the Promotion of Science. All three authors were partially supported by CNRS Grant PICS No. 7270.

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