LIAONING NORMAL UNIV, DEPT PHYS, DALIAN 116029, PEOPLES R CHINA
; ACAD SINICA, INST HIGH ENERGY PHYS, BEIJING 100039, PEOPLES R CHINA
Racah coefficients of O(n) and Sp(2m) are derived from subduction coefficients of Brauer algebras D-f(n) by using the Schur-Weyl duality relation between D-f(n) and O(n) or Sp(2m). It is found that there are two types of Racah coefficients according to irreps of O(n) or Sp(2m) with or without trace contraction. It is proved that Racah coefficients with no trace contraction in the irreps are trivial and the same as those of unitary groups U(n), which are rank n-independent, and those with trace contraction usually are n-dependent. Racah coefficients with trace contraction for the resulting irreps [n(1),n(2),n(3), 0 over dot] with Sigma(i=1)(3) n(i) less than or equal to 3 are tabulated.