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Clebsch-Gordan coefficients of \(\mathrm{SU}(3)\) with simple symmetry properties. (English) Zbl 0601.22015

If the representations of a compact Lie group \(G\) are given in matrix form then a tensor product of irreducible representations of \(G\) is decomposed into irreducible constituents by means of the matrix. Its elements are called Clebsch-Gordan coefficients. For groups of rank \(r>1\) irreducible representations may enter the tensor product with multiplicities \(n>1\). In this case Clebsch-Gordan coefficients are not uniquely defined.
Using the infinitesimal operators the authors construct the operator which separates the multiple representations in the tensor product for the case of the group \(\mathrm{SU}(3)\). This allows to fix Clebsch-Gordan coefficients. The symmetry properties of these coefficients are derived. They are similar to those of \(\mathrm{SU}(2)\) Clebsch-Gordan coefficients. The algebraic algorithm for the coefficients is given.
Reviewer: A.Klimyk

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Citations:

Zbl 0601.22016
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