Higher symmetries of the conformal powers of the Laplacian on conformally flat manifolds
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://jmp.aip.org/resource/1/jmapaq/v53/i3/p032301_s1?isAuthorized=no |
| Doi | http://dx.doi.org/10.1063/1.3692324 |
| Field | General mathematics |
| Keywords | differential equations - mathematical operators - tensors - symmetries |
| 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 dimension at least 3. In particular, this yields all symmetries of the powers of the Laplacian on Euclidean space. The algebra formed by the symmetry operators is described explicitly. |
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