Description
The vector space of Killing tensors forms a module of the Lie algebra of global symmetries. Since the classification of global reducibility parameters is generically easier than the classification of global symmetries, this fact can be used to constrain the latter when knowing the former. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal.