| 初等表示的权的标积 |
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| 引用本文： | 李光华.初等表示的权的标积[J].电工标准与质量,1988(4). |
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| 作者姓名： | 李光华 |
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| 作者单位： | 长沙水电师院物理系 |
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| 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.
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| 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.THE SCALAR PRODUCT OF THE WEIGHTS FOR THE ELEMENTARY REPRESENTATION[J].Journal of Changsha University of Electric Power(Natural Science Edition),1988(4). |
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| Authors: | Li Guanghua |
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| Affiliation: | Physics Department |
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| Abstract: | The simple roots for any semi-simple Lie algebra can be represented by the weights of appropriate elementary representation.Conversely,the weights for the elementary representation can also be represented by simple roots.When the set of roots for a semi-simple Lie algebra have been selected appropriately,the scalar product of the weights of the elementary representation can be calculated. In this paper by using cartan matrix,a method for calculating the scalar product of the weights of the elementary representation for semi- simple Lie algebra is presented,and from this,the eigen value of the second Casimir operator is worked out. |
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| Keywords: | Dynkin diagram elementary representatiom Casimir operator |
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