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Résumé : We study representations of the Schrodinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using the correspondence we compute analytically the energy of up to six fermions at unitarity in a harmonic potential near two and four spatial dimensions. We also compute the energy of up to four anyons in a harmonic potential near the bosonic and fermionic limits.