[en] The authors try to solve the following problems: provided that variation freedom is not restricted and intragroup correlation is taken into account in a given approximation, is it possible to develop for group functions any analogue of the well known (in the case of orbitals) Adams-Gilbert-Kunz method that could give one a possibility to go from delocalized group functions to localized ones seeking for minimization of the intergroup correlation? 20 refs, 1 tab

[en] The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators Θ_λ are represented using particular values (at specially chosen Ξ = Ξ_o) of the Radon transform D_Nλ D_Nλ(Ξ) of the N-DM spatial parts (or their sums) D_Nλ(χ'|χ double-prime) (here, Ξ is a d-plane in the n-space Re double-prime of χ = (χ', χ double-prime), with n = 6N, d = 3(N - k), χ' double-bond ' (r'₁,...,r_N'), χ double-prime double-prime triple-bond (r₁ double-prime,...,r_N double-prime)). In this way, the problem is reduced to investigation of the properties of the functions D_Nλ(Ξ). For a normalizable N - DM, it is proved that D_Nλ(Ξ) are bounded functions. The properties of D_Nλ(Ξ) implied by the N-DM permutational symmetry, Hermiticity, and positive definiteness are found. A formal procedure of reconstruction of all N-DM corresponding to a given k-RDM is proposed. 38 refs