On harmonic superspaces and superconformal fields in four dimensions

Representations of four-dimensional superconformal groups on harmonic super fields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplet s may admit several descriptions as superfields on different superspaces. I n particular, this is the case for on-shell massless superfields. This allo ws a description of short representations as explicit products of fundament al fields. Superconformal transformations of analytic fields in real harmon ic superspaces are given explicitly.