Abstract
For pt.I see ibid vol.20, p.769-84, 1987. The new solution to the SU(n) external state labelling problem, proposed in the first paper of this series, is analysed in detail in the SU(3) case in terms of the two complementary chains U(3)*U(3) contains/implies U(3) and U(2, 2) contains/implies U(2)*U(2). The classification of SU(3) coupled states is completed by the labels of an intermediate U(2) irreducible representation hs=(hs1hs2), directly related to King's branching rule for U( 3)*U(3)U(3). For pedagogical purposes, the SU(2) coupled state construction, based upon the complementary chains U(2)*U(2) contains/implies U(2) and U(1, 1) contains/implies U(1)*U(1), is considered first. For both SU(2) and SU(3), it is proved that, in addition to the standard recursion relations, the corresponding Wigner coefficients satisfy recursion relations of a different type, arising from the action of the U(1, 1) or U(2, 2) complementary group generators. A detailed example shows that such complementary recursion relations are quite useful for numerical purposes.
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