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

Abstract

Analytical inversion symmetry of the biorthogonal systems of SU4 contains/implies SU2 × Su2, SUn contains/implies SOn and Sp4 contains/implies U2 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 SUn contains/implies SOn for couplings (p0) × (0q) to (λ 0 μ) and (p10) × (p20) to (λ ν 0), as well as the resubducing coefficients (transformation brackets) for expansion of the SU3 contains/implies SO3 Elliott basis states and Sp4 contains/implies U2 Smirnov and Tolstoy basis states in terms of the corresponding canonical basis states. New expressions for bilinear combinations of SUn contains/implies SOn special isofactors are obtained. Expansion of SU3 canonical basis states in terms of SU3 contains/implies SO3 Elliott states is found. Isofactors for coupling of two Elliott states are given.