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We give a new fusion procedure for the Brauer algebra by showing that all primitive idempotents can be found by evaluating a rational function in several variables. The function takes values in the Brauer algebra and has the form of a product of  R -matrix type factors. In particular, this provides a one-parameter version of the fusion procedure for the symmetric group. The  R -matrices are solutions of the Yang–Baxter equation associated with the classical Lie algebrasof types  B ,  C , and  D . Moreover, we construct an evaluation homomorphism from a reflection equation algebratoand show that the fusion procedure provides an equivalence between natural tensor representations ofwith the corresponding evaluation modules.

A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms