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Generating functions encoding cubic interactions of (partially-)masslesshigher-spin fields are provided within the ambient-space formalism. Theysatisfy a system of higher-order partial differential equations that can beexplicitly solved due to their factorized form. We find that the number ofconsistent couplings increases whenever the squares of the field masses takesome integer values (in units of the cosmological constant) and satisfy certainconditions. Moreover, it is shown that only the supplemental solutions can giverise to non-Abelian deformations of the gauge symmetries. The presence of theseconditions on the masses is a distinctive feature of (A)dS interactions thathas in general no direct counterpart in flat space.

Generating functions of (partially-)massless higher-spin cubic interactions