标题： 广义卡西米尔算子和群的张量表示 显示英文标题

标题： The generalized Casimir operator and tensor representations of groups

摘要： 已经提出了一种新的方法，用于通过广义Casimir算子构造李群张量表示空间的基本函数。 在该算子的定义中，使用了李导数而不是相应的无穷小算子。 在引入广义Casimir算子时，我们使用了一个度量，使得所考虑的群是等距的，这由广义Casimir算子的不变性条件得出。 这使我们能够正确地表述特征值和特征函数问题。 为了分离不可约成分，已经构造了不变投影算子。 作为例子，考虑了Bianchi类型G^3 IX和G^3 II群。 显示英文摘要

摘要： There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the Lie derivatives instead of the corresponding infenitisemal operators. When introducing the generalized Casimir operator we use the metric for which a group being considered will be isometry that follows from the invariance condition for the generalized Casimir operator. This allows us to formulate the eigenvalue and eigenfunction problems correctly. The invariant projection operators have been constructed in order to separate irreducible components. The cases of the Bianchi type G^3 IX and G^3 II groups are considered as examples.