Orthogonalization of the SU(n)superset of SO(n) projected states and SU(3)superset of U(2) isofactors

The explicit direct and inverse orthogonalization coefficients (OCs) are derived for the projected basis states of the two parametric covariant irreducible representations of SU(n) superset of SO(n) (including Elliott's n = 3 case) and SU(4) superset of SU(2) x SU(2) (Draayer), with the alternative choices of the Gram-Schmidt processes, began, respectively, from the lowest (Vergados) or highest absolute value of the intrinsic parameter K. The different direct and inverse OCs (the latter equivalent to the definite boundary SU(n) superset of SO(n) isofactors, or the boundary resubducing coefficients) are found to be connected by the definite analytical continuation-contraction procedures with mutually related OCs of the biorthogonal SU(3) x SU(3) superset of SU(3) states and the boundary orthonormal pseudocanonical and paracanonical isofactors of SU(3) superset of U(2). The orthogonalization coefficients considered are presented as definite algebraic-polynomial structures under the square root, with the linear factors and numerator-denominator polynomials in terms of the partition-dependent functions of Biedenharn and Louck, A(lambda)((a,b,d,e)(c)).