The induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)
Pan, Feng ; Dong, Shi-hai ; Draayer, J. P.
arXiv, 9803045 / Harvested from arXiv
Text on arXiv
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 .
Publié le : 1998-03-30
Classification:  Mathematical Physics 
@article{9803045,
     author = {Pan, Feng and Dong, Shi-hai and Draayer, J. P.},
     title = {The induced representations of Brauer algebra and the Clebsch-Gordan
  coefficients of SO(n)},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9803045}
}

Pan, Feng; Dong, Shi-hai; Draayer, J. P. The induced representations of Brauer algebra and the Clebsch-Gordan
  coefficients of SO(n). arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9803045/