Short representations of SU(2,2/N) and harmonic superspace analyticity

We consider the harmonic superspaces associated with SU(2, 2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] 'elementary' ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k = 1...[N/2]) with top spin J(top) = (N/2 - k/2, 0). For N = 2n, we analyze UIR's obtained by tensoring the self-conjugate ultrashort multiplet J(top) = (n/2, 0) and show that N - 1 different basic products give rise to all possible UIR's with residual shortening.