A new fusion procedure for the Brauer algebra and evaluation homomorphisms

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

2011-01-07

arxiv.org/abs/1101.1336v1

Mathematics

Representation Theory

31 pages

Scientific paper

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 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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