Superalgebra for M theory on a pp wave

We study the superalgebra of the M theory on a fully supersymmetric pp wave. We identify the algebra as the special unitary Lie superalgebra, (Formula presented) or (Formula presented) and analyze its root structure. We discuss the typical and atypical representations deriving the typicality condition explicitly in terms of the energy and other four quantum numbers. We classify the BPS multiplets preserving 4, 8, 12, 16 real supercharges and obtain the corresponding spectrum. We show that in the BPS multiplet either the lowest energy floor is an (Formula presented) singlet or the highest energy floor is an (Formula presented) singlet.