Idempotents for Birman-Murakami-Wenzl algebras and reflection equation. (English) Zbl 1343.17010

Summary: 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.


17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16T25 Yang-Baxter equations
20C08 Hecke algebras and their representations
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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