THE BIEDENHARN-LOUCK-HECHT RESOLUTION OF THE OUTER MULTIPLICITY PROBLEM FOR THE U(3) AND U-Q(3) GROUPS

The solution of the outer multiplicity problem in the tensor product o f U(3) irreducible representations (irreps) developed by Biedenharn et al.((1-7)) and realized through the well-known Draayer-Akiyama (DA) c omputer code((8)) is extended to the quantum algebra U-q(3). An analyt ic formula for special stretched U-q(3) Wigner coefficients, [(lambda( 1) mu(1)) H-1, (lambda(2) mu(2)) epsilon(2) Lambda(2)m(2)\(lambda(3) m u(3)) H-3](max)(q) is derived using a projection operator method.((9-1 0)) In this expression H-i denotes the highest weight vector of the (l ambda(i) mu(i)) irrep; the subscript ''max'' means coefficients corres ponding to a unit tensor operator with a maximal characteristic null s pace; and q is the usual quantum label so the standard U(3) Wigner coe fficient, which is required in the DA code, can be obtained in the q - -> 1 limit of the theory. To illustrate the theory, some U-q(3) Wigner coefficients for the tensor product (22) x (22) are calculated. The p rocedure for evaluating nonhighest weight Wigner U-q(3) coefficients f ollow the DA prescription.