## A new fusion procedure for the Brauer algebra and evaluation homomorphisms

### A. P. Isaev, A. I. Molev and O. V. Ogievetsky

#### Abstract

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 which has the form of a product of $R$-matrix type factors. In particular, this provides a new fusion procedure for the symmetric group involving an arbitrary parameter. The $R$-matrices are solutions of the Yang–Baxter equation associated with the classical Lie algebras $g_N$ of types $B$, $C$ and $D$. Moreover, we construct an evaluation homomorphism from a reflection equation algebra $B(g_N)$ to $U(g_N)$ and show that the fusion procedure provides an equivalence between natural tensor representations of $B(g_N)$ with the corresponding evaluation modules.

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 Monday, January 17, 2011