A new rule for computing Clebsch-Gordan series

AbstractA new combinatorial rule for computing the Clebsch-Gordan series of a tensor product of irreducible SU(n)-representations is introduced. This rule provides an efficient algorithm for computing features of the Clebsch-Gordan multiplicities, such as the “characteristic nullspaces” of tensor operators, that are not easily computed by other methods. Furthermore, unlike the Littlewood-Richardson rule, this new rule generalizes, in principle, to other semisimple Lie groups. This generalization and its consequences for tensor operators are discussed in some detail. As an application, it is shown that as n increases, it is possible to find characteristic nullspaces for SU(n)-tensor operators, which have arbitrarily large multiplicity