We investigate the graded structure of the tensor product space V(lamb
da 2)xV(lambda 1), which arises in the coupling of two irreducible rep
resentations lambda(1) and lambda(2) of a semisimple Lie algebra G, in
the limit in which one of the highest weights becomes asymptotically
large. The construction of asymptotic coupling coefficients is conside
red. (C) 1998 American Institute of Physics. [S0022-2488(98)01002-0].