狄拉克符号在有限群表示论中的应用

The applications of dirac notations in representation theory of finite groups

根据量子力学中狄拉克符号适用于线性空间理论这一性质,作者将该符号体系用于有限群表示论中,首先得到左正则表示与右正则表示的普遍关系.然后在该符号体系帮助下更深刻的理解正交性定理与完备性定理,并且推导出正交性定理的第二种形式.最后重新表述特征标相关理论,并在此基础上讨论特征标第二正交关系与正交性定理第二种形式间的联系.

Because the Dirac notations are applicable to theories of linear space, the authors apply such notations to representation theory of finite groups. The general relations between left and right regular representations are obtained firstly. Then with the help of such notations more profound comprehension is acquired in the orthogonality theorem and the completeness relation, and the second orthogonality relation is derived either. Finally based on re-expressing theories for characters, the relations between second orthogonality relation for characters and the second orthogonality relation are also discussed.