Some coupling and recoupling coefficients for symmetric representations of SOn

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Abstract
A new expression of SOn contains/implies SOn-1 isoscalar factors (reduced Wigner coefficients) for coupling l1*l2 to (L1L2) is obtained. Special classes of these factors (including those used together with special isofactors of SUn contains/implies SOn in On-scalar basis functions depending on the microscopic collective variables of a nucleus) are shown as being proportional to the 6j-coefficients of SU2 with standard or quartervalued parameters. Group chain reflection symmetry of isofactors is discovered which allows the author to interchange certain reflected parameters of irreducible representations of the group and its subgroup. Recoupling coefficients (6l-coefficients) for symmetric representations of SOn (n>or=5) are expanded in terms of 6j-coefficients of SU2 with standard or quartervalued parameters. New expressions for special Clebsch-Gordan and 6j-coefficients of SU2(SO3) are presented.