Yf. Smirnov et Yi. Kharitonov, Solving the multiplicity problem in the direct product of irreducible representations of su(3) and su(q)(3) algebras by diagonalizing Gram matrices, PHYS ATOM N, 62(7), 1999, pp. 1094-1098
A method for solving the multiplicity problem in the direct product of irre
ducible representations of the su(3) and su(q)(3) algebras is described. Th
is method is based on diagonalizing the Gram matrix for a set of originally
nonorthonormalized vectors. By considering the example of the direct produ
ct (Il) x (ll), it is shown that this method provides a natural solution to
the problem of splitting the degenerate irreducible representations of the
su(q)(3) quantum algebra, yielding elegant analytic expressions for Wigner
coefficients at small degeneracy multiplicities.