The induced representations of Brauer algebras and the Clebsch-Gordan coefficients of SO(n)

Feng Pan; Shihai Dong; J. P. Draayer

doi:10.1088/0305-4470/31/40/016

The induced representations of Brauer algebras and the Clebsch-Gordan coefficients of SO(n)

Feng Pan, Shihai Dong, J. P. Draayer

Research output: Contribution to journal › Article › peer-review

Abstract

Induced representations of D_f(n) from S_f1 × S_f2 with f₁ + f₂ = f are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients of S_f1 × S_f2 ↑ D_f (n ) with f ≤ 4 up to a normalization factor are derived by using the linear equation method. Weyl tableaux for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining Clebsch-Gordan coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebras is proposed. Some isoscalar factors of SO(n) ⊃ SO(n - 1) for the resulting irrep [λ₁, λ₂, λ₃, λ₄, 0̇] with ∑⁴_i=1 λi ≤ 4 are tabulated.

Original language	English
Pages (from-to)	8247-8266
Number of pages	20
Journal	Journal of Physics A: Mathematical and General
Volume	31
Issue number	40
DOIs	https://doi.org/10.1088/0305-4470/31/40/016
State	Published - 9 Oct 1998
Externally published	Yes

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title = "The induced representations of Brauer algebras and the Clebsch-Gordan coefficients of SO(n)",

abstract = "Induced representations of Df(n) from Sf1 × Sf2 with f1 + f2 = f are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients of Sf1 × Sf2 ↑ Df (n ) with f ≤ 4 up to a normalization factor are derived by using the linear equation method. Weyl tableaux for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining Clebsch-Gordan coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebras is proposed. Some isoscalar factors of SO(n) ⊃ SO(n - 1) for the resulting irrep [λ1, λ2, λ3, λ4, {\.0}] with ∑4i=1 λi ≤ 4 are tabulated.",

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AU - Draayer, J. P.

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N2 - Induced representations of Df(n) from Sf1 × Sf2 with f1 + f2 = f are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients of Sf1 × Sf2 ↑ Df (n ) with f ≤ 4 up to a normalization factor are derived by using the linear equation method. Weyl tableaux for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining Clebsch-Gordan coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebras is proposed. Some isoscalar factors of SO(n) ⊃ SO(n - 1) for the resulting irrep [λ1, λ2, λ3, λ4, 0̇] with ∑4i=1 λi ≤ 4 are tabulated.

AB - Induced representations of Df(n) from Sf1 × Sf2 with f1 + f2 = f are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients of Sf1 × Sf2 ↑ Df (n ) with f ≤ 4 up to a normalization factor are derived by using the linear equation method. Weyl tableaux for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining Clebsch-Gordan coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebras is proposed. Some isoscalar factors of SO(n) ⊃ SO(n - 1) for the resulting irrep [λ1, λ2, λ3, λ4, 0̇] with ∑4i=1 λi ≤ 4 are tabulated.

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The induced representations of Brauer algebras and the Clebsch-Gordan coefficients of SO(n)

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