UNITARY SUPERMULTIPLETS OF OSP(1 32,R) AND M-THEORY/

We review the oscillator construction of the unitary representations o f non-compact groups and supergroups and study the unitary supermultip lets of OSp(1/32, R) in relation to M-theory. OSp(1/32, R) has a singl eton supermultiplet consisting of a scalar and a spinor field. Parity invariance leads us to consider OSp(1/32, R)(L) x OSp(1/32, R)(R) as t he ''minimal'' generalized AdS supersymmetry algebra of M-theory corre sponding to the embedding of two spinor representations of SO(10, 2) i n the fundamental representation of Sp(32, R). The contraction to the Poincare superalgebra with central charges proceeds via a diagonal sub supergroup OSp(1/32, R)(L-R) which contains the common subgroup SO(10, 1) of the two SO(10,2) factors. The parity invariant singleton superm ultiplet of OSp(1/32, R)(L) x OSp(1/32, R)(R) decomposes into an infin ite set of ''doubleton'' supermultiplets of the diagonal OSp(1/32,R)(L -R). There is a unique ''CPT self-conjugate'' doubleton supermultiplet whose tensor product with itself yields the ''massless'' generalized AdS(11) supermultiplets. The massless graviton supermultiplet contains fields corresponding to those of eleven-dimensional supergravity plus additional ones. Assuming that an AdS phase of M-theory exists we arg ue that the doubleton field theory must be the holographic superconfor mal field theory in ten dimensions that is dual to M-theory in the sam e sense as the duality between the N = 4 super-Yang-Mills in d = 4 and the IIB superstring over AdS(5) x S-5. (C) 1998 Elsevier Science B.V.