The induced representations of Brauer algebras and the Clebsch-Gordan coefficients of SO(n)
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.
Publication Source (Journal or Book title)
Journal of Physics A: Mathematical and General
Pan, F., Dong, S., & Draayer, J. (1998). The induced representations of Brauer algebras and the Clebsch-Gordan coefficients of SO(n). Journal of Physics A: Mathematical and General, 31 (40), 8247-8266. https://doi.org/10.1088/0305-4470/31/40/016