Massive gravitino propagator in maximally symmetric spaces and fermions in dS/CFT

We extend the method of calculation of propagators in maximally symmetric spaces (Minkowski, dS, AdS and their euclidean versions) in terms of intrinsic geometric objects to the case of massive spin 3/2 field. We obtain the propagator for arbitrary space-time dimension and mass in terms of Heun's function, which is a generalization of the hypergeometric function appearing in the case of other spins. As an application of this result we calculate the conformal dimension of the dual operator in the recently proposed dS/CFT correspondence both for spin 3/2 and for spin 1/2. We find that, in agreement with the expectation from analytic continuation from AdS, the conformal dimension of the dual operator is always complex (i.e. it is complex for every space-time dimension and value of the mass parameter). We comment on the implications of this result for fermions in dS/CFT.