Prolongation of symmetric Killing tensors and commuting symmetries of   the Laplace operator
  We determine the space of commuting symmetries of the Laplace operator on pseudo-Riemannian manifolds of constant curvature, and derive its algebra structure. Our construction is based on the Riemannian tractor calculus, allowing to construct a prolongation of the differential system for symmetric Killing tensors. We also discuss some aspects of its relation to projective differential geometry. 
J.-P. Michel, P. Somberg and J. \v{S}ilhan
math.DG