Cubic interactions of higher spins in (A)dS

Cubic interactions of massive and partially-massless totally-symmetric higher-spin fields in any constant-curvature background of dimension greater than three are investigated. Making use of the ambient-space formalism, the consistency condition for the traceless and transverse parts of the parity-invariant interactions is recast into a system of partial differential equations. The general solutions are expressed in a compact form as generating functions of all the consistent couplings. The Stueckelberg formulation of the cubic interactions as well as their massless limits are also analyzed.