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We give a new fusion procedure for the Brauer algebra by showing that allprimitive idempotents can be found by evaluating a rational function in severalvariables which has the form of a product of R-matrix type factors. Inparticular, this provides a new fusion procedure for the symmetric groupinvolving an arbitrary parameter. The R-matrices are solutions of theYang--Baxter equation associated with the classical Lie algebras g_N of typesB, C and D. Moreover, we construct an evaluation homomorphism from a reflectionequation algebra B(g_N) to U(g_N) and show that the fusion procedure providesan equivalence between natural tensor representations of B(g_N) with thecorresponding evaluation modules.

A new fusion procedure for the Brauer algebra and evaluation homomorphisms