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We give the classification of the positive energy (lowest weight) unitaryirreducible representations of the superalgebras osp(1|2n,R).Comment: 20 pages, LATEX2e (revtex4,amsmath,amssymb), Plenary talk by VKD at X  International Conference on Symmetry Methods in Physics, Yerevan,  13-21.8.2003; added acknowledgements; corrected misprint

Positive energy unitary irreducible representations of the superalgebras osp(1|,2n, ℝ)