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

Irreducible representations of Birman-Wenzl algebras C-f (r, q) in the nons tandard basis are discussed. A procedure for evaluating subduction coeffici ents (SDCs), or the transformation coefficients between standard and non-st andard basis of Birman-Wenzl algebras, is formulated based on the linear. e quation method. SDCs of C-f (r, q) with f less than or equal to 4 are deriv ed. Racah coefficients of the quantum groups O-q (n) and Sp(q) (2m) can be obtained from SDCs of Birman-Wenzl algebras C-f (r, q) by using the Schur-W eyl-Brauer duality relation between Birman-Wenzl algebras C-f (r, q) and th e quantum groups O-q (n) and Sp(q) (2m).