【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。更多还原

【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.更多还原