  A Killing-Yano tensor is an antisymmetric tensor obeying a first-order
differential constraint similar to that obeyed by a Killing vector. In this
article we consider generalisations of such objects, focusing on the conformal
case. These generalised conformal Killing-Yano tensors are of mixed symmetry
type and obey the constraint that the largest irreducible representation of
$o(n)$ contained in the tensor constructed from the first-derivative applied to
such an object should vanish. Such tensors appear naturally in the context of
spinning particles having $N_0=1$ worldline supersymmetry and in the related
problem of higher symmetries of Dirac operators. Generalisations corresponding
to extended worldline supersymmetries and to spacetime supersymmetry are
discussed.
