Non-canonical subgroup restrictions of the unitary group U(nm)decreases monotonically to a limit U(n) x U(m)

A reduction of the inner product space of the permutation group on an N-particle system has been used to develop a scheme for obtaining the states spanning a general irreducible representation of the unitary group U(nm) in terms of those spanning the product representations of U(n) x U(m). Since relatively straightforward methods are now available for determining the Clebsch-Gordan coefficients for the permutation groups, the present procedure is viable. As special cases of the general expression, algebraic expressions for the reduction of identity and alternating representations of U(nm) are obtained. (author)