Symmetries in Science VII 1994
DOI: 10.1007/978-1-4615-2956-9_28
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Dynamical Symmetries in the sdg Interacting Boson Model

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(9 citation statements)
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“…For η > 2 the use of formulae given in section 2 allows one to compute {η} 3 ⊗ {m} for any η and m. From these calculations one realizes that the number of multiplets (λ, μ) as well as their multiplicities D (λ,μ) {η},{m} grow very fast with increasing η and m. For example, for η = 4 and m = 20 one has 566 multiplets with multiplicities as big as 3148 while for η = 5 and m = 20 those numbers are 879 and 187 328. This justifies the search for a statistical law for equation (1). Now we will give a preview.…”
Section: Introductionmentioning
confidence: 92%
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“…For η > 2 the use of formulae given in section 2 allows one to compute {η} 3 ⊗ {m} for any η and m. From these calculations one realizes that the number of multiplets (λ, μ) as well as their multiplicities D (λ,μ) {η},{m} grow very fast with increasing η and m. For example, for η = 4 and m = 20 one has 566 multiplets with multiplicities as big as 3148 while for η = 5 and m = 20 those numbers are 879 and 187 328. This justifies the search for a statistical law for equation (1). Now we will give a preview.…”
Section: Introductionmentioning
confidence: 92%
“…A statistical law for the multiplicities D(m, L) of the SO(3) irreps [L] in the reduction of totally symmetric irreducible representations (irreps) {m} of U(N ) in U(N ) → SO (3), with the basic association {1} U(N ) → i [ i ]⊕, i.e. number of times the irrep L appears in {m} → L, is well known [1,2]. This has been derived both by using the 'plethysm' formulation of the problem [3] and by using the SO(2) subgroup of SO (3) [1,4].…”
Section: Introductionmentioning
confidence: 99%
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