Canonical solution of the state labelling problem for SU(n)⊃SO(n) and Littlewood's branching rule. II. Use of modification rules

For pt.I see ibid., vol.16, p.2095 (1983). In part I it was shown that when d<or=( 1 / 2 n), the internal state labelling problem for the d-row irreducible representations of SU(n), when reduced with respect to SO(n), amounts to the external state labelling problem for U(d). This result is now extended to the d>( 1 / 2 n) case, where Littlewood's branching rule (1950) for U(n) contains/implies O(n) has to be supplemented with Newell's modification rules (1951). The explicit solution of the state labelling problem for (v+1)-row irreducible representations of both SU(2v+1) and SU(2v) is given and is shown to reflect the operation of Littlewood's modified branching rule in a direct way. The generalisation to higher d values is then outlined.