Subduction coefficients of Brauer algebras and Racah coefficients of O( n) and Sp(2 m): II. Racah coefficients

Racah coefficients of O(n) and Sp(2m) are derived from subduction coefficients of Brauer algebras by using the Schur - Weyl duality relation between 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 with are tabulated.