  At the core of nonperturbative theories of quantum gravity lies the
holographic encoding of bulk data in large matrices. At present this mapping is
poorly understood. The plane wave matrix model provides a laboratory for
isolating aspects of this problem in a controlled setting.
  At large boosts, configurations of concentric membranes become superselection
sectors, whose exact spectra are known. From the bulk point of view one expects
product states of individual membranes to be contained within the full
spectrum. However, for non-BPS states this inclusion relation is obscured by
Gauss law constraints. Its validity rests on nontrivial relations in
representation theory, which we identify and verify by explicit computation.
