A finite subgroup of the exceptional Lie group G2
A finite subgroup of the exceptional Lie group G2
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例外李群 G2 的有限子群
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
B. G. Wybourne
中科院分区：
文献类型：
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作者：
R. King;F. Toumazet;B. G. Wybourne
为了进一步完善特殊群G2在原子和核光谱学中的应用，我们证实了对称群S8的一个168阶的简单有限群L168~PSL2(7)也是G2的一个子群。通过特征理论和其他方法证明了L168在G2中有两个不同的嵌入，类似于SO(3)在G2中的两个不同的嵌入。给出了相关分支规则、张量积和对称张量积的表格。作为进一步应用的激励，给出了L168对八面体结晶点群O的约束的分支规则。
With a view to further refining the use of the exceptional group G2 in atomic and nuclear spectroscopy, it is confirmed that a simple finite subgroup L168~PSL2(7) of order 168 of the symmetric group S8 is also a subgroup of G2. It is established by character theoretic and other methods that there are two distinct embeddings of L168 in G2, analogous to the two distinct embeddings of SO(3) in G2. Relevant branching rules, tensor products and symmetrized tensor products are tabulated. As a stimulus to further applications the branching rules are given for the restriction from L168 to the octahedral crystallographic point group O.