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