Reduction of inner-product representations of unitary groups

Abstract

A direct method for the reduction of inner products of irreducible representations (irreps) of unitary groups has been proposed using the duality between the permutation and unitary groups. A canonical tensor basis set has been used to obtain a closed expression for the Clebsch–Gordan coefficients of U(n). This expression involves the subduction coefficients arising in the outer-product reduction of SN1⊗SN2→SN1+N2 of the permutation groups, the symmetrization coefficients of U(n), and matrix elements of the standard representation of SN. The expression holds good for an inner-product reduction of irreps of U(n), and is independent of n. The method has been illustrated with examples.