Article (Scientific journals)
Higher Symmetries of the Laplacian via Quantization
Michel, Jean-Philippe
2014In Annales de l'Institut Fourier, 64
Peer reviewed
 

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Keywords :
Symmetry algebra, Laplacian, Quantization; Conformal geometry; Minimal nilpotent orbit, Symplectic reduction
Abstract :
[en] We develop a new approach, based on quantization methods, to study higher symmetries of invariant di erential operators. We focus here on conformally invariant powers of the Laplacian over a conformally at manifold and recover results of Eastwood, Leistner, Gover and ilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic ow and the algebra of higher symmetries of the conformal Laplacian. Combined with a symplectic reduction, this leads to a quantization of the minimal nilpotent coadjoint orbit of the conformal group. The star-deformation of its algebra of regular functions is isomorphic to the algebra of higher symmetries of the conformal Laplacian. Both identify with the quotient of the universal envelopping algebra by the Joseph ideal.
Disciplines :
Mathematics
Author, co-author :
Michel, Jean-Philippe ;  Université du Luxembourg > Département de mathématique
Language :
English
Title :
Higher Symmetries of the Laplacian via Quantization
Publication date :
2014
Journal title :
Annales de l'Institut Fourier
ISSN :
0373-0956
eISSN :
1777-5310
Publisher :
Institut Fourier, Grenoble, France
Volume :
64
Pages :
à paraître
Peer reviewed :
Peer reviewed
Name of the research project :
AFR grant PDR-09-063.
Funders :
Luxembourgian NRF
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since 06 January 2014

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