On the decomposition rules of tensor products of the representations of the classical Weyl groups
On the decomposition rules of tensor products of the representations of the classical Weyl groups
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经典Weyl群表示的张量积的分解规则
DOI：
10.1016/0021-8693(84)90072-3
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发表时间：
1984
影响因子：
0.9
通讯作者：
T. Tokuyama
中科院分区：
文献类型：
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作者：
T. Tokuyama
对称群的表示理论与称为杨氏图的划分符号有着很好的联系。G. de. B。罗宾逊给出了对称群表示的张量积分解规则，即计算对称群的两个任意不可约表示的张量积表示的不可约分支重数的算法。其他经典Weyl群的表示理论由Specht，Mayer等人进行了研究，可以用“划分对”来描述。迈耶给出了一个聪明的建设的不可约表示使用外尔子群。本文给出了经典Weyl群表示的张量积的分解规则。我们通常使用字符而不是表示本身。我们的基本方法如下。设W是一个经典Weyl群。首先，我们选择一个子群族，称为“nice”子群，并选择“nice”子群中的一些字符，我们称之为“nice”子群的“handy”字符。接下来我们证明了“nice”子群族和“handy”特征标满足以下三个条件。
The representation theory of the symmetric group is beautifully related with the partition symbols called Young diagrams. G. de. B. Robinson gave the decomposition rule of tensor products of the representations of the symmetric groups, ie, an algorithm to calculate the multiplicities of the irreducible constituents of tensor product representation of two arbitrary irreducible representations of a symmetric group. The representation theory of the other classical Weyl groups were studied by Specht, Mayer and others, which can be described by means of ‘pairs of partitions. Mayer gave a smart construction of the irreducible representations using Weyl subgroups. In this paper we shall give the decomposition rules of tensor products of the representations of the classical Weyl groups. We usually use character instead of representation itself. Our basic method is the following. Let W be a classical Weyl group. First we choose a family of subgroups called “nice” subgroups, and also choose some characters of the “nice” subgroups which we call the “handy” characters of the “nice” subgroups. Next we show that the family of “nice” subgroups and the “handy” characters satisfy the followng three conditions.