Brauer代数中标准基到非标准基变换的组合学
Combinatorics of transformations from standard to non-standard bases in Brauer algebras
摘要：
考虑了Brauer中心化代数$\mathfrak{B}_f(x)$的不可约表示的标准基与适合于$\mathfrak{B}_{f_1} (x) \times \mathfrak{B}_{f_2} (x) \subset \mathfrak{B}_f (x)$子代数（$f_1 +f_2 = f$）的分裂基之间的变换系数.在给出适当的组合背景之后，基于俯冲网格节点上的$i$ -耦合关系的定义，我们引入了一个广义的俯冲图，它扩展了J.Phys.A：Math. Gen. $\mathbf{39}$ 7657-7668中关于对称群的俯冲图.这样，我们就可以描述由线性方法产生的俯冲系统的结构，并给出解空间形式的轮廓。在网格上的排序关系也给出，然后，在对称群的情况下，相的选择和管理的多重分离的自由因子进行了讨论。
英文摘要：
Transformation coefficients between standard bases for irreducible representations of the Brauer centralizer algebra $\mathfrak{B}_f(x)$ and split bases adapted to the $\mathfrak{B}_{f_1} (x) \times \mathfrak{B}_{f_2} (x) \subset \mathfrak{B}_f (x)$ subalgebra ($f_1 +f_2 = f$) are considered. After providing the suitable combinatorial background, based on the definition of $i$-coupling relation on nodes of the subduction grid, we introduce a generalized version of the subduction graph which extends the one given in J. Phys. A: Math. Gen. $\mathbf{39}$ 7657-7668 for symmetric groups. Thus, we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space. An ordering relation on the grid is also given and then, as in the case of symmetric groups, the choices of the phases and of the free factors governing the multiplicity separations are discussed.
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