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

Lianrong Dai, Liaoning Normal University
Feng Pan, Liaoning Normal University
J. P. Draayer, Louisiana State University


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.