Seed conformal blocks in 4D CFT

We compute in closed analytical form the minimal set of seed conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (l, (l) over bar,) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0, vertical bar l - (l) over bar vertical bar) and one(vertical bar l - (l) over bar vertical bar, 0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (l, (l) over bar), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p = vertical bar l - (l) over bar vertical bar and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories.