A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms

作者：Isaev A P; Molev A I^*; Ogievetsky O V

来源：International Mathematics Research Notices, 2012, (11): 2571-2606.

DOI：10.1093/imrn/rnr126

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. The function takes values in the Brauer algebra and has the form of a product of R-matrix type factors. In particular, this provides a one-parameter version of the fusion procedure for the symmetric group. 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.

• 出版日期2012