  Representations of four-dimensional superconformal groups on harmonic
superfields are discussed. It is shown how various short representations can be
obtained by parabolic induction. It is also shown that such short multiplets
may admit several descriptions as superfields on different superspaces. In
particular, this is the case for on-shell massless superfields. This allows a
description of short representations as explicit products of fundamental
fields. Superconformal transformations of analytic fields in real harmonic
superspaces are given explicitly.
