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

a new method is proposed for constructing the complete set of irreducible representations of conformal supergroup of SU(2,2/1) acting on superfields of the PHIsub(k) (x, THETAsub(+), THETAsub(-) type (k is the Lorentz index, THETAsub(+), THETAsub(-) are the 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(1,4)OSp1(1,4) of the SU(2,2/1) supergroup. These spaces are those closed also with respect to another OSp(1,4) subgroup OSp2(1,4) which intersects with OSp1(1,4) over 0(2,3) and completes it to the whole SU(2,2/1). The precise criterion for selecting such invariant spaces is formulated. New series of SU(2,2/1) representations are found, and the problem of equivalency between representations induced by different little (super) groups is discussed