Preprint

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 gN of types B, C and D. Moreover, we construct an evaluation homomorphism from a reflection equation algebra B(gN) to U(gN) and show that the fusion procedure provides an equivalence between natural tensor representations of B(gN) with the corresponding evaluation modules.

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Monday, January 17, 2011