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We give a constructive classification of the positive energy (lowest weight)unitary irreducible representations of the D=6 superconformal algebrasosp(8*/2N). Our results confirm all but one of the conjectures of Minwalla (forN=1,2) on this classification. Our main tool is the explicit construction ofthe norms of the states that has to be checked for positivity. We give also thereduction of the exceptional UIRs.Comment: 27 pages, TeX with harvmac, amssym.def, amssym.tex; v.2: minor  corrections and references added; v.3: minor corrections; v.4: to appear in  J. Phys.

Positive energy unitary irreducible representations of D $equal$ 6 conformal supersymmetry