A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms
A New Fusion Procedure for the Brauer Algebra and Evaluation Homomorphisms
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DOI：
10.1093/imrn/rnr126
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发表时间：
2011-01
影响因子：
1
通讯作者：
A. Isaev;A. Molev;O. Ogievetsky
中科院分区：
文献类型：
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作者：
A. Isaev;A. Molev;O. Ogievetsky
我们给出了一个新的融合程序的Brauer代数的所有原始幂等元可以找到通过评估一个有理函数在几个变量。该函数取布劳尔代数中的值，并且具有R-矩阵型因子的乘积的形式。特别是，这提供了一个单参数版本的对称群的融合过程。R-矩阵是与B、C和D型经典李代数相关的杨-巴克斯特方程的解。此外，我们构造了一个评价同态从反射方程代数，并表明，融合过程提供了一个等价的自然张量表示与相应的评价模块。
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 of types B, C, and D. 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.