  We derive the spectrum of gauge invariant operators for maximally
supersymmetric Yang-Mills theories in d dimensions. After subtracting the tower
of BPS multiplets, states are shown to fall into long multiplets of a hidden
SO(10,2) symmetry dressed by thirty-two supercharges. Their primaries organize
into a universal, i.e. d-independent pattern. The results are in perfect
agreement with those following from (naive) KK reduction of type II strings on
the warped AdS x S near-horizon geometry of Dp-branes.
