A complete system of pairwise orthogonal minimal idempotents for Birman-Murakami-Wenzl algebras is obtained by a consecutive evaluation of a rational function in several variables on sequences of quantum contents of up-down tableaux. A by-product of the construction is a one-parameter family of fusion procedures for Hecke algebras. Classical limits to two different fusion procedures for Brauer algebras are described.
"Idempotents for Birman–Murakami–Wenzl algebras and reflection equation." Adv. Theor. Math. Phys. 18 (1) 1 - 25, January 2014.