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We give character formulae for the positive energy unitary irreduciblerepresentations of the N-extended D=4 conformal superalgebras su(2,2/N). Usingthese we also derive decompositions of long superfields as they descend to theunitarity threshold. These results are also applicable to irreps of the complexLie superalgebras sl(4/N). Our derivations use results from the representationtheory of su(2,2/N) developed already in the 80s.Comment: 81 pages, input files: harvmac, amssym.def, amssym.tex; corrected  misprint

Characters of the positive energy UIRs of D = 4 conformal supersymmetry