# Subduction coefficients of Birman-Wenzl algebras and Racah coefficients of the quantum groups Oq(n) and Spq(2m): II. Racah coefficients

#### Abstract

Racah coefficients of Oq(n) and Spq(2m) are derived from subduction coefficients of Birman-Wenzl algebras Cf(r, q) by using the Schur-Weyl-Brauer duality relation between Birman-Wenzl algebras Cf(r, q) with r = qn-1 or q-2m-1 and the quantum group Oq(n) or Spq(2m). It is shown that there are two types of the Racah coefficients according to irreps of Oq(n) or Spq(2m) with or without q-deformed trace contraction. The Racah coefficients without q-deformed trace contraction in the irreps involved are n-independent, and are the same as those of quantum groups Uq(n). As examples, Racah coefficients of Oq(n) with q-deformed trace contraction for the resulting irreps [n1, n2, 0̇] with n1 + n2 ≤ 2 are tabulated, which are also Racah coefficients of Spq(2m) with substitution n → -2m and conjugation of the corresponding irreps.

*This paper has been withdrawn.*