General construction of the unitary representations of anti-de sitter superalgebras and the spectrum of the S⁴ compactification of 11-dimensional supergravity

We construct the spectrum of the S⁴ 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 S⁴ compactification.