Subduction coefficients of Birman-Wenzl algebras and Racah coefficients of the quantum groupsOq(n) andSpq(2m): I. Subduction coefficients

Abstract

Irreducible representations of Birman-Wenzl algebras Cf (r,q) in the non-standard basis are discussed. A procedure for evaluating subduction coefficients (SDCs), or the transformation coefficients between standard and non-standard basis of Birman-Wenzl algebras, is formulated based on the linear equation method. SDCs of Cf (r,q) with f ⩽ 4 are derived. Racah coefficients of the quantum groups Oq(n) and Spq(2m) can be obtained from SDCs of Birman-Wenzl algebras Cf (r,q) by using the Schur-Weyl-Brauer duality relation between Birman-Wenzl algebras Cf (r,q) and the quantum groups Oq(n) and Spq(2m).