  Under the hypotheses of smoothness in the coupling constant, locality,
Lorentz covariance, and Poincare invariance of the deformations, combined with
the preservation of the number of derivatives on each field, the consistent
interactions between a single free massless tensor gauge field with the mixed
symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector
field have been investigated. The computations are done with the help of the
deformation theory based on a cohomological approach, in the context of the
antifield-BRST formalism. The main result is that there exist nontrivial
cross-couplings between these types of fields in five spatiotemporal
dimensions, which break the PT invariance and allow for the deformation of the
gauge transformations of the vector field, but not of the gauge algebra.
