On the phase space of free higher-spin theories and conformal transformations

We write a first order action for higher-spin fields and construct a canonical map to Fronsdal theory. The first-order description is defined over complex field configurations and has conformal invariance. We show that it is possible to push forward these transformations to a set of symmetries in Fronsdal theory that satisfies the conformal algebra but is not given by standard conformal change of coordinates.