  Recent investigations have revealed powerful selection rules for resonant
energy transfer between modes of non-linear perturbations in global anti-de
Sitter (AdS) space-time. It is likely that these selection rules are due to the
highly symmetric nature of the underlying AdS background, though the precise
relation has remained unclear. In this article, we demonstrate that the
equation satisfied by the scalar field mode functions in AdS(d+1) has a hidden
SU(d) symmetry, and explicitly specify the multiplets of this SU(d) symmetry
furnished by the mode functions. We also comment on the role this structure
might play in explaining the selection rules.
