A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms

Abstract

We give a new fusion procedure for the Brauer algebra by showing that all\nprimitive idempotents can be found by evaluating a rational function in several\nvariables which has the form of a product of R-matrix type factors. In\nparticular, this provides a new fusion procedure for the symmetric group\ninvolving an arbitrary parameter. The R-matrices are solutions of the\nYang--Baxter equation associated with the classical Lie algebras g_N of types\nB, C and D. Moreover, we construct an evaluation homomorphism from a reflection\nequation algebra B(g_N) to U(g_N) and show that the fusion procedure provides\nan equivalence between natural tensor representations of B(g_N) with the\ncorresponding evaluation modules.\n