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Higher symmetries of the conformal powers of the Laplacian on conformally flat manifolds

Gover, A. Rod; Šilhan, Josef

Description

On locally conformally flat manifolds, we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the property that they are symmetries of any natural conformally invariant differential operator between such bundles. These are used to construct all symmetries of the conformally invariant powers of the Laplacian (often called the GJMS operators) on manifolds of...[Show more]

dc.contributor.authorGover, A. Rod
dc.contributor.authorŠilhan, Josef
dc.date.accessioned2015-09-22T00:11:31Z
dc.date.available2015-09-22T00:11:31Z
dc.identifier.issn0022-2488
dc.identifier.urihttp://hdl.handle.net/1885/15616
dc.description.abstractOn locally conformally flat manifolds, we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the property that they are symmetries of any natural conformally invariant differential operator between such bundles. These are used to construct all symmetries of the conformally invariant powers of the Laplacian (often called the GJMS operators) on manifolds of dimension at least 3. In particular, this yields all symmetries of the powers of the Laplacian Δ k , k∈Z>0, on Euclidean space En. The algebra formed by the symmetry operators is described explicitly.
dc.description.sponsorshipA.R.G. gratefully acknowledges support from the Royal Society of New Zealand via Marsden Grant Nos. 06-UOA-029 and 10-UOA-113. J.S. was supported by the Max-Planck-Institute fur Math- ¨ ematik in Bonn and by the Grant agency of the Czech republic under the Grant No. P201/12/G028.
dc.publisherAmerican Institute of Physics
dc.rightshttp://www.sherpa.ac.uk/romeo/issn/0022-2488..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 22/09/15). Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics and may be found at https://doi.org/10.1063/1.3692324
dc.sourceJournal of Mathematical Physics
dc.titleHigher symmetries of the conformal powers of the Laplacian on conformally flat manifolds
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume53
dc.date.issued2012-03-21
local.identifier.absfor010108
local.identifier.absfor010501
local.identifier.ariespublicationf5625xPUB2967
local.publisher.urlhttps://www.aip.org/
local.type.statusPublished Version
local.contributor.affiliationGover, Rod, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
local.contributor.affiliationSilhan, Josef, Masaryk University, Czech Republic
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage032301
local.identifier.doi10.1063/1.3692324
local.identifier.absseo970101
dc.date.updated2015-12-11T07:49:30Z
local.identifier.scopusID2-s2.0-84859313015
local.identifier.thomsonID000302387300014
CollectionsANU Research Publications

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