Abstract. We consider generalized conformal supersymmetry constructed as parabose N = 4 algebra. It is shown that sacrificing of manifest Lorentz covariance leads to interpretation of the generalized conformal supersymmetry as a symmetry that contains, on equal footing, two "rotation" groups. The necessary symmetry breaking is briefly considered. A connection is then established between Green's Ansatz and multiparticle spaces, and some relations with spin-statistics connection are pointed out.

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