Biorthogonal systems for SU₄⊃SU₂× SU₂, SUn⊃SOnand Sp₄⊃U₂and analytical inversion symmetry

Analytical inversion symmetry of the biorthogonal systems of SU 4 contains/implies SU 2 × Su 2 , SU n contains/implies SO n and Sp 4 contains/implies U 2 bases for two-parametric (covariant and mixed tensor) irreducible representation is discovered. This symmetry relates the dual isoscalar factors or resubducing coefficients. It allowed us to invert, by means of a special analytical continuation procedure, the non-orthogonal isofactors of SU n contains/implies SO n for couplings (p0) × (0q) to (λ 0 μ) and (p 1 0) × (p 2 0) to (λ ν 0), as well as the resubducing coefficients (transformation brackets) for expansion of the SU 3 contains/implies SO 3 Elliott basis states and Sp 4 contains/implies U 2 Smirnov and Tolstoy basis states in terms of the corresponding canonical basis states. New expressions for bilinear combinations of SU n contains/implies SO n special isofactors are obtained. Expansion of SU 3 canonical basis states in terms of SU 3 contains/implies SO 3 Elliott states is found. Isofactors for coupling of two Elliott states are given.