Generalized Einstein operator generating functions

We present gauge invariant, self-adjoint Einstein operators for mixed symmetry higher spin theories. The result applies to multi-forms, multi-symmetric forms and mixed antisymmetric and symmetric multi-forms, generalizing previous results for combinations of these cases. It also yields explicit action principles for these theories in terms of their minimal covariant field content. For known cases, these actions imply the mixed symmetry equations of motion of Labastida. The result is based on a calculus for handling normal ordered operator expressions built from quantum generators of the underlying constraint algebras.