The structure of N=3 multiplets in AdS(4) and the complete Osp(3 vertical bar 4) x SU(3) spectrum of M-theory on AdS(4) x N-0,N-1,N-0

In this paper, relying on previous results of one of us on harmonic analysi s, we derive the complete spectrum of Osp(3/4) x SU(3) multiplets that one obtains compactifying D = 11 supergravity on the unique homogeneous space N -0,N-1,N-0 that has a tri-sasakian structure, namely leads to N = 3 supersy mmetry both in the four-dimensional bulk and on the three-dimensional bound ary. As in previously analyzed cases the knowledge of the Kaluza-Klein spec trum, together with general information on the geometric structure of the c ompact manifold is an essential ingredient to guess and construct the corre sponding superconformal field theory. This is work in progress. As a bonus of our analysis we derive and present the explicit structure of all unitary irreducible representations of the superalgebra Osp(3/4) with maximal spin content s(max) less than or equal to 2. (C) 1999 Published by Elsevier Sci ence B.V. All rights reserved.