  It is shown that all the states in AdS(5) x S(5) supergravity have zero
eigenvalue for the all Casimir operators of its symmetry group SU(2,2|4). To
compute this universal zero in supergravity we refine the oscillator methods
for studying the lowest weight unitary representations of SU(N,M|R,S). We solve
the reduction problem when one multiplies an arbitrary number of super
doubletons. This enters in the computation of the quadratic Casimir eigenvalues
of the lowest weight representations. We apply the results to SU(2,2|4) that
classifies the Kaluza-Klein towers of ten dimensional type IIB supergravity
compactified on AdS(5) x S(5). We show that the vanishing of the SU(2,2|4)
Casimir eigenvalues for all the states is indeed a group theoretical fact in
AdS(5) x S(5) supergravity. By the AdS-CFT correspondence, it is also a fact
for gauge invariant states of super Yang-Mills theory with four supersymmetries
in four dimensions. This non-trivial and mysterious zero is very interesting
because it is predicted as a straightforward consequence of the fundamental
local Sp(2) symmetry in 2T-physics. Via the 2T-physics explanation of this zero
we find a global indication that this special supergravity hides a twelve
dimensional structure with (10,2) signature.
