Weight multiplicities for the classical groups
Weight multiplicities for the classical groups
复制标题
经典群的权重重数
DOI：
--
复制
发表时间：
1976
期刊：
影响因子：
--
通讯作者：
R. King
中科院分区：
文献类型：
--
作者：
R. King
与从U（k）到Tk的子群链相关的分支规则首先由Delaney和Gruber（4）用于计算权重多重性，他们利用了本文描述的模式和表格的联系。Gilmore（12，13）提出了对其他经典群的推广，但他没有得到这里看到的提供计算权重多重性的最有效方法的推广的Young表。使用这些表格的最大优点是，对于任意秩的群很容易得到结果。Plunkett（14）已经编制了相当多的关于群O（n）的张量和旋量表示的结果表。希望在其他地方发表这些结果以及U（k）和Sp（2k）的类似结果。
The branching rule associated with the subgroup chain leading from U(k) to Tk was first used to calculate weight multiplicities by Delaney and Gruber(4), who exploited the connection with patterns and tableaux described here. The generalisation to the other classical groups was suggested by Gilmore(12,13) who did not however arrive at the generalised Young tableaux which are seen here to provide the most efficient means of calculating weight multiplicities. The great merit of using these tableaux is that results are readily obtained for groups of arbitrary rank. Considerable tables of results for the tensor and spinor representations of the groups O(n) have been compiled by Plunkett(14). It is hoped to published these, and similar results for U(k) and Sp(2k)), elsewhere.