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On locally conformally flat manifolds we describe a construction which mapsgeneralised conformal Killing tensors to differential operators which may acton any conformally weighted tensor bundle; the operators in the range have theproperty that they are symmetries of any natural conformally invariantdifferential operator between such bundles. These are used to construct allsymmetries of the conformally invariant powers of the Laplacian (often calledthe GJMS operators) on manifolds of dimension at least 3. In particular thisyields 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 thesymmetry operators is described explicitly.

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