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

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 $f\le 4$ 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}λ_{i}\leq .

48 pages latex, submitted to Journal of Phys. A

References in corpus (1)

• A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)