The representation theory of the maximally extended superalgebra with 32
fermionic and 528 bosonic generators is developed in order to investigate
non-perturbative properties of the democratic secret theory behind strings and
other p-branes. The presence of Lorentz non-singlet central extensions is
emphasized, their role for understanding up to 13 hidden dimensions and their
physical interpretation as boundaries of p-branes is elucidated. The criteria
for a new larger set of BPS-like non-perturbative states is given and the
methods of investigation are illustrated with several explicit examples.Comment: Latex, 18 papge
