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

Understand

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 $\Delta^k$, $k\in \mathbb{Z}>0$, on Euclidean space $\mathbb{E}^n$.
• The algebra formed by the symmetry operators is described explicitly.