On Haantjes tensors for second-order superintegrable systems

The vanishing of the Haantjes tensor is an important property that has been linked, for instance, to the existence of separation coordinates and the integrability of systems of hydrodynamic type. We discuss the vanishing of the Haantjes tensor for operator fields that admit a large number of so-called conservation laws. In particular, we investigate Haantjes-zero Killing tensor fields that are associated with second-order superintegrable systems.