Standard Young tableaux and weight multiplicities of the classical Lie groups
Standard Young tableaux and weight multiplicities of the classical Lie groups
复制标题
经典李群的标准杨氏画面和权重重数
DOI：
10.1088/0305-4470/16/14/012
复制
发表时间：
1983
期刊：
影响因子：
--
通讯作者：
N. G. El
中科院分区：
文献类型：
--
作者：
R. King;N. G. El
通过检查限制为 U(1)*U(1)*U(1) 的经典群 U(k)、SU(k)、SO(2k+1)、Sp(2k) 和 SO(2k) 的所有不可约表示的分支规则，为每个群指定了标准 Young 画面。结果表明，这些画面决定了不可约表示的相应特征。推导了构建这些画面的规则，并且通过这种方式，权重重数的确定被简化为简单的组合练习。给出了这种权重重数的一般公式，涵盖了最困难的情况：即 SO(2k) 的公式。提供了说明性示例，包括一些产生权重重数的显式 k 依赖性的示例。
By examining the branching rules for all irreducible representations of the classical groups U(k), SU(k), SO(2k+1), Sp(2k) and SO(2k) on restriction to U(1)*U(1)*U(1), standard Young tableaux are specified for each of these groups. It is shown that these tableaux determine the corresponding characters of the irreducible representations. The rules for constructing these tableaux are derived and in this way the determination of weight multiplicities is reduced to a simple combinatorial exercise. General formula for such weight multiplicities are given encompassing the most difficult case: namely that of SO(2k). Illustrative examples are provided, including some yielding the explicit k-dependence of weight multiplicities.