Scalar factors for non-canonical subgroup restriction of unitary group

A procedure has been outlined for obtaining the scalar factors (reduced Wigner coefficients) of the unitary group U(nm)containsU(n)xU(m). This has been done at the permutation group level for Ssub(N)downSsub(N')xSsub(N'') and the equality between the scalar factors of these two groups has been exploited. It has been shown that the scalar factors can be uniquely expressed in terms of the inner and outer product coupling coefficients of the permutation group. The ambiguity due to multiplicity is resolved at the level of the above coefficients. (author)