Two general results applicable to the problem of a canonical definition of the Wigner coefficient in Un are demonstrated: (1) the existence of a canonical imbedding of Un × Un into Un2 and (2) a general factorization lemma for operators defined in the boson calculus. Using these results, a resolution of the multiplicity problem for U3 is demonstrated, in which all degenerate operators are shown to split completely upon projection into U2.
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Biedenharn et al. (1967) studied this question.
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