Subduction coefficients of Birman-Wenzl algebras and Racah coefficients ofthe quantum groups O-q(n) and Sp(q)(2m): II. Racah coefficients

Racah coefficients of O-q (n) and Sp(q) (2m) are derived from subduction co efficients of Birman-Wenzl algebras C-f (r, q) by using the Schur-Weyl-Brau er duality relation between Birman-Wenzl algebras C-f (r, q) with r = q(n-1 ) or q(-2m-1) and the quantum group O-q (n) or Sp(q) (2m). It is shown that there are two types of the Racah coefficients according to irreps of O-q ( n) or SPq (2m) with or without q-deformed trace contraction. The Racah coef ficients without q-deformed trace contraction in the irreps involved are n- independent, and are the same as those of quantum groups U-q (n). As exampl es, Racah coefficients of O-q (n) with q-deformed trace contraction for the resulting irreps [n(1), n(2), 0] with n(1) + n(2) less than or equal to 2 are tabulated, which are also Racah coefficients Of SPq (2m) with substitut ion n --> -2m and conjugation of the corresponding irreps.