A new fusion procedure for the Brauer algebra and evaluation homomorphisms

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.

31 pages

References in corpus (3)

• On the idempotents of Hecke algebras
• Representations of twisted Yangians associated with skew Young diagrams
• A mixed hook-length formula for affine Hecke algebras

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• The Brauer Category and Invariant Theory
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• A note on degenerate cyclotomic Yokonuma-Hecke algebras
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• Manin matrices of type C: multi-parametric deformation
• Fusion procedure for Degenerate cyclotomic Hecke algebras
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