  A complementary group to SU(n) is found that realizes all features of the
Littlewood rule for Kronecker products of SU(n) representations. This is
accomplished by considering a state of SU(n) to be a special Gel'fand state of
the complementary group {\cal U}(2n-2). The labels of {\cal U}(2n-2) can be
used as the outer multiplicity labels needed to distinguish multiple
occurrences of irreducible representations (irreps) in the SU(n)\times
SU(n)\downarrow SU(n) decomposition that is obtained from the Littlewood rule.
Furthermore, this realization can be used to determine SU(n)\supset
SU(n-1)\times U(1) Reduced Wigner Coefficients (RWCs) and Clebsch-Gordan
Coefficients (CGCs) of SU(n), using algebraic or numeric methods, in either the
canonical or a noncanonical basis. The method is recursive in that it uses
simpler RWCs or CGCs with one symmetric irrep in conjunction with standard
recoupling procedures. New explicit formulae for the multiplicity for SU(3) and
SU(4) are used to illustrate the theory.
