All positive energy unitary irreducible representations of extended conformal supersymmetry

We give the list of all positive energy UIR's of the conformal superalgebra su(2,2/N). They are realized as subrepresentations of elementary representations. The latter are induced from irreducible finite-dimensional Lorentz and su(N) representations on spaces of functions (superfields). Some of the unitary representation spaces are comprised from solutions of invariant differential equations. Among these the massless UIR's are discussed in detail. (orig.)