Formalism of gauge invariant curvatures and constructing the cubic   vertices for massive spin-3/2 field in AdS_4 space
  We study the interaction of massive spin-3/2 field with electromagnetic and gravitational fields in the four dimensional AdS space and construct the corresponding cubic vertices. Construction is based on generalization of Fradkin-Vasiliev formalism, developed for massless higher spin fields, to massive fermionic higher spin fields. The main ingredients of this formalism are the gauge invariant curvatures. We build such curvatures for the massive theory under consideration and show how the cubic vertices are written in their terms. 
I. L. Buchbinder, T. V. Snegirev, Yu. M. Zinoviev
hep-th