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Non-trivial, consistent interactions of a free, massless tensor field t_{\mu\nu |\alpha \beta} with the mixed symmetry of the Riemann tensor are studied inthe following cases: self-couplings, cross-interactions with a Pauli-Fierzfield and cross-couplings with purely matter theories. The main results,obtained from BRST cohomological techniques under the assumptions onsmoothness, locality, Lorentz covariance and Poincar\'{e} invariance of thedeformations, combined with the requirement that the interacting Lagrangian isat most second-order derivative, can be synthesized into: no consistentself-couplings exist, but a cosmological-like term; no cross-interactions withthe Pauli-Fierz field can be added; no non-trivial consistent cross-couplingswith the matter theories such that the matter fields gain gauge transformationsare allowed.Comment: for version 3: 45 pages, uses amssymb; shortened version, the three  appendices from version 2 can be found in hep-th/040209

Interactions of a massless tensor field with the mixed symmetryof the Riemann tensor. No-go results