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In this paper by means of harmonic analysis we derive the complete spectrumof Osp(2|4) x SU(2) x SU(2) x SU(2) multiplets that one obtains compactifyingD=11 supergravity on the homogeneous space Q^{111}. In particular we analyzethe structure of the short multiplets and compare them with the correspondingcomposite operators of the N=2 conformal field theory dual to such acompactification, found in a previous publication. We get complete agreementbetween the quantum numbers of the supergravity multiplets on one side andthose of the conformal operators on the other side, confirming the structure ofthe conjectured SCFT. However the determination of the actual spectrum byharmonic analysis teaches us a lot more: indeed we find out which multipletsare present for each representation of the isometry group, how many they are,the exact values of the hypercharge and of the energy for each multiplet.Comment: 31 page

classical and quantum gravity

M-theory on AdS 4 × Q 111 : the complete Osp (2|4)× SU (2)× SU (2)× SU (2) spectrum from harmonic analysis