  In this paper we derive the projectors to all irreducible SO(d)
representations (traceless mixed-symmetry tensors) that appear in the partial
wave decomposition of a conformal correlator of four stress-tensors in d
dimensions. These projectors are given in a closed form for arbitrary length
$l_1$ of the first row of the Young diagram. The appearance of Gegenbauer
polynomials leads directly to recursion relations in $l_1$ for seed conformal
blocks. Further results include a differential operator that generates the
projectors to traceless mixed-symmetry tensors and the general normalization
constant of the shadow operator.
