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, su(2|4;2,0) or su(2|4;2,4), 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 su(2) singlet or the highest energy floor is an su(4) singlet.