THE INDUCED REPRESENTATIONS OF BRAUER ALGEBRAS AND THE CLEBSCH-GORDAN-COEFFICIENTS OF SO(N)

Induced representations of D-f(n) from S-f1 x S-f2 with f(1) + f(2) = f are discussed. The induction coefficients (IDCs) or the outer-produc t reduction coefficients of S-f1 x S-f2 up arrow D-f(n) with f less th an or equal to 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 Cleb sch-Gordan coefficients of SO(n) in the Gel'fand basis for no modifica tion rule involved couplings from IDCs of Brauer algebras is proposed. Some isoscalar factors of SO(n) superset of SO(n - 1) for the resulti ng irrep [lambda(1), lambda(2), lambda(3), lambda(4), 0] with Sigma(i= 1)(4) lambda(i) less than or equal to 4 are tabulated.