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

We consider the harmonic superspaces associated to 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 $J_{\mathrm{t}\mathrm{o}\mathrm{p}}=(N\mathrm{/}2-k\mathrm{/}2,0)$. For N=2n we analyze UIR’s obtained by tensoring the self-conjugate ultrashort multiplet $J_{\mathrm{t}\mathrm{o}\mathrm{p}}$= (n/2,0) and show that N-1 different basic products give rise to all possible UIR’s with residual shortening.