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| 初等表示的权的标积 | |
| 引用本文： | 李光华. 初等表示的权的标积[J]. 长沙理工大学学报(社会科学版), 1988, 0(4) |
| 作者姓名： | 李光华 |
| 作者单位： | 长沙水电师院物理系 |
| 摘 要： | 半单李代数的素根可以用适当的初等表示的权来表示,反过来,初等表示的权也可以用素根来表示。在适当地选取了半单李代数的根系之后,就可算出初等表示权的标积。本文利用Cartan矩阵给出了一种计算半单李代数初等表示的权的标积的方法,并由此算出了二次Casimir算符的本征值。 |
| 关 键 词： | Dynkin图 初等表示 Casimir算符 |
THE SCALAR PRODUCT OF THE WEIGHTS FOR THE ELEMENTARY REPRESENTATION |
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| Li Guanghua Physics Department. THE SCALAR PRODUCT OF THE WEIGHTS FOR THE ELEMENTARY REPRESENTATION[J]. Journal of Changsha University of Science & Technology, 1988, 0(4) | |
| Authors: | Li Guanghua Physics Department |
| Affiliation: | Li Guanghua Physics Department |
| Abstract: | The simple roots for any semi-simple Lie algebra can be representedby the weights of appropriate elementary representation. Conversely, theweights for the elementary representation can also be repeesented by simpleroots. When the set of roots for a semi-simple Lie algehra have beenselected appropriately, the scalar product of the weights of the elementaryrepresentation can be calculated. In this paper by using cartan matrix, a method for calculating thescalar product of the weights of the elementary representation for semi-simple Lie algebra is presented, and from this, the eigen value of the aecondCasimir operator is worked out. |
| Keywords: | Dynkin diagram elementary representatiom Casimir operator |
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