  We generalize the embedding formalism for conformal field theories to the
case of general operators with mixed symmetry. The index-free notation encoding
symmetric tensors as polynomials in an auxiliary polarization vector is
extended to mixed-symmetry tensors by introducing a new commuting or
anticommuting polarization vector for each row or column in the Young diagram
that describes the index symmetries of the tensor. We determine the tensor
structures that are allowed in n-point conformal correlation functions and give
an algorithm for counting them in terms of tensor product coefficients. A
simple derivation of the unitarity bound for arbitrary mixed-symmetry tensors
is obtained by considering the conservation condition in embedding space. We
show, with an example, how the new formalism can be used to compute conformal
blocks of arbitrary external fields for the exchange of any conformal primary
and its descendants. The matching between the number of tensor structures in
conformal field theory correlators of operators in d dimensions and massive
scattering amplitudes in d+1 dimensions is also seen to carry over to
mixed-symmetry tensors.
