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

DOI10.1063/1.3692324zbMATH Open1274.35063arXiv0911.5265OpenAlexW1989218899MaRDI QIDQ2861780

Author name not available (Why is that?)

Publication date: 11 November 2013

Published in: (Search for Journal in Brave)

Abstract: 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

D e l t a^{k}

,

k i n m a t h b b Z > 0

, on Euclidean space

m a t h b b E^{n}

. The algebra formed by the symmetry operators is described explicitly.

Full work available at URL: https://arxiv.org/abs/0911.5265

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