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 Δ k , k∈Z>0, on Euclidean space En. The algebra formed by the symmetry operators is described explicitly.A.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
