Projectors and seed conformal blocks for traceless mixed-symmetry tensors

In this paper we derive the projectors to all irreducible SO(d) representations ( (t)raceless 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.