ON THE DECOMPOSITION OF THE UNITARY-GROUP AND THE MULTIPLE COUPLING OF ANGULAR MOMENTA

The decomposition of the direct product group, S-n X U-N, for a system of n identical particles having access to N one-particle states is co nsidered from the point of view of its reduction to invariant subspace s. A double-factor matrix approach is developed in terms of the freque ncy of occurrence of the invariant subspaces and the frequency of conf igurations arising from the set of one-particle states. Simple formula s are obtained for both these frequencies. It is shown that this appro ach is especially useful when treating the problem of multiple couplin g of the quantum numbers of the states. (C) 1997 John Wiley & Sons, In c.