dorsal/arxiv
View SchemaThe induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)
| Authors | Feng Pan, Shi-hai Dong, J. P. Draayer |
|---|---|
| Categories | |
| ArXiv ID | physics/9803045 |
| URL | https://arxiv.org/abs/physics/9803045 |
| DOI | 10.1088/0305-4470/31/40/016 |
| Journal | J.Phys.A31:8247-8266,1998 |
Abstract
Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times S_{f_{2}}\uparrow D_{f}(n)$ with $f\leq 4$ up to a normalization factor are derived by using the linear equation method. Weyl tableaus for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining CG coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebra are proposed. Some isoscalar factors of $SO(n)\supset SO(n-1)$ for the resulting irrep $[\lambda_{1},~\lambda_{2},~ \lambda_{3},~\lambda_{4},\dot{0}]$ with $\sum\limits_{i=1}^{4}\lambda_{i}\leq .
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"abstract": "Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\\times\nS_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients\n(IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\\times\nS_{f_{2}}\\uparrow D_{f}(n)$ with $f\\leq 4$ up to a normalization factor are\nderived by using the linear equation method. Weyl tableaus for the\ncorresponding Gel\u0027fand basis of SO(n) are defined. The assimilation method for\nobtaining CG coefficients of SO(n) in the Gel\u0027fand basis for no modification\nrule involved couplings from IDCs of Brauer algebra are proposed. Some\nisoscalar factors of $SO(n)\\supset SO(n-1)$ for the resulting irrep\n$[\\lambda_{1},~\\lambda_{2},~ \\lambda_{3},~\\lambda_{4},\\dot{0}]$ with\n$\\sum\\limits_{i=1}^{4}\\lambda_{i}\\leq .",
"arxiv_id": "physics/9803045",
"authors": [
"Feng Pan",
"Shi-hai Dong",
"J. P. Draayer"
],
"categories": [
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/31/40/016",
"journal_ref": "J.Phys.A31:8247-8266,1998",
"title": "The induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)",
"url": "https://arxiv.org/abs/physics/9803045"
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