Abstract (Elsevier)
We construct the spectrum of the S 4 compactification of d = 11 supergravity by simple algebraic methods. The spectrum consists of a special class of positive-energy unitary irreducible representations of the supergroup Osp (8 ∗ /4) = Osp (6, 2 4 ) , the so-called short supermultiplets. This paper shows how to obtain easily all such representations of the supergroup Osp ( 8 ∗ 4 ) . We find that there is an ultra-short supermultiplet, the doubleton, which is analogous to the singleton of Osp ( 8 4 , R ) . The method described here can be used to obtain all positive-energy unitary supermultiplets of Osp ( 8 ∗ 4) and not just those that aise in the S 4 compactification.