  We show how conformal partial waves (or conformal blocks) of spinor/tensor
correlators can be related to each other by means of differential operators in
four dimensional conformal field theories. We explicitly construct such
differential operators for all possible conformal partial waves associated to
four-point functions of arbitrary traceless symmetric operators. Our method
allows any conformal partial wave to be extracted from a few "seed"
correlators, simplifying dramatically the computation needed to bootstrap
tensor correlators.
