Unitary supermultiplets of OSp(8/4,R) and the spectrum of the S7 compactification of 11-dimensional supergravity

The spectrum of the S7 compactification of 11-dimensional supergravity is constructed very simply by using the oscillator method. The spectrum consists of a special class of positive energy unitary irreducible representations (UIR's) of the N=8 anti-de Sitter supergroup OSp(8/4,R). This class of UIR's correspond to the short supermultiplets whose spin range is 2. The ultra-short supermultiplet, the singleton, whose spin range is 1/2 has no Poincare limit and does not occur in the spectrum. The method described here can be used to obtain all positive energy unitary supermultiplets of OSp(8/4,R) and not just those that arise in the S7 compactification. In addition, the oscillator method can be used to obtain the positive energy UIR's of the non-compact supergroups OSp(2n/2m,R), OSp(2nsup(*)/2m) and SU(n,m/p). (orig.)