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

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

1998-03-30

arxiv.org/abs/physics/9803045v1

J.Phys.A31:8247-8266,1998

Physics

Mathematical Physics

48 pages latex, submitted to Journal of Phys. A

Scientific paper

10.1088/0305-4470/31/40/016

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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