Higher Symmetries of the Laplacian via Quantization

Details Higher Symmetries of the Laplacian via Quantization Higher Symmetries of the Laplacian via Quantization

2011-07-28

arxiv.org/abs/1107.5840v2

Mathematics

Differential Geometry

20 pages, minor improvements

Scientific paper

We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold, and recover results of Eastwood, Leistner, Gover and Silhan. In particular, conformally equivariant quantization establishes a crystal clear correspondence between hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Resorting to symplectic reduction, this leads to a quantization of the minimal nilpotent coadjoint orbit of the conformal group and allows to identify the latter algebra of symmetries in terms of the Joseph ideal. By the way, we obtain a tangential star-product for a family of coadjoint orbits of the conformal group.

Affiliated with

Also associated with

No associations

Rating

Higher Symmetries of the Laplacian via Quantization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Higher Symmetries of the Laplacian via Quantization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher Symmetries of the Laplacian via Quantization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-318236