The structure of N=3 multiplets in AdS₄ and the complete Osp(3|4) X SU(3) spectrum of M-theory on AdS₄ X N⁰¹⁰

In this paper, relying on previous results of one of us on harmonic analysis, 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^{0,1,0} that has a tri-sasakian structure, namely leads to N=3 supersymmetry both in the four-dimensional bulk and on the three-dimensional boundary. As in previously analyzed cases the knowledge of the Kaluza Klein spectrum, together with general information on the geometric structure of the compact manifold is an essential ingredient to guess and construct the corresponding 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}>=2.