Structure of representations of the conformal supergroup in the $OSp(1,4)$ basis

A new method is suggested for constructing the complete set of irreducible representations of conformal supergroup $SU(2,2/1)$ acting on superfields of the type $\Phi(k,\theta_+,\theta_-)$ ($k$ being the Lorentz index, $\theta_+$, $\theta_-$ left- and right-handed Grassmann coordinates). Its main point is the reduction of the problem to the much more simple task of extracting the minimal set of certain invariant spaces of the orthosymplectic subgroup $OSp^\mathrm{I}(1,4)$, of the supergroup $SU(2,2/1)$. These spaces are those closed also with respect to another $OSp(1,4)$-subgroup ($OSp^\mathrm{II}(1,4)$) which intersects with $OSp^\mathrm{I}(1,4)$ over $O(2,3)$ and completes it to the whole $SU(2,2/1)$. The precise criterion for selection of such invariant spaces is formulated. New series of $SU(2,2/1)$ representations are found and the problem of the equivalency between representations induced by various little (super) groups is discussed.