Gravitational cubic interactions for a massive mixed symmetry gauge field

In a recent paper (Boulanger et al 2011 J. Phys. A: Math. Theor. 44 415403), cubic gravitational interactions for a massless mixed symmetry field in an AdS space have been constructed. In the current paper, we extend these results to the case of massive field. We work in a Fradkin-Vasiliev approach and use a frame-like gauge-invariant description for the massive field which works in the AdS spaces with arbitrary values of the cosmological constant including a flat Minkowski space. In this, the massless limit in the AdS space coincides with the results of Boulanger et al (2011) while we show that it is impossible to switch on a gravitational interaction for the massless field in the dS space. (paper)