X iv : h ep - t h / 04 06 15 4 v 4 4 S ep 2 00 5 Characters of the Positive Energy UIRs of D = 4 Conformal Supersymmetry

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of su(2,2/N) developed already in the 80s.