Massless Poincaré modules and gauge invariant equations

Starting with an indecomposable Poincaré module M0 induced from a given irreducible Lorentz module we construct a free Poincaré invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides with (in general, is closely related to) the starting point module M0. We show that for a class of indecomposable Poincaré modules the resulting theory is a Lagrangian gauge theory of the mixed-symmetry higher spin fields. The procedure is based on constructing the parent formulation of the theory. The Labastida formulation and the unfolded description of the mixed-symmetry fields are reproduced through the appropriate reductions of the parent formulation. As an independent check we show that in the momentum representation the solutions form a unitary irreducible Poincaré module determined by the respective module of the Wigner little group.