  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,\bar l) of the Lorentz group in
four dimensional conformal field theories. These blocks arise from 4-point
functions involving two scalars, one (0,|l-\bar l|) and one (|l-\bar l|,0)
spinors or tensors. We directly solve the set of Casimir equations, that can
elegantly be written in a compact form for any (l,\bar l), 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=|l-\bar l | 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.
