A recursive method for the construction of irreducible representations of the orthogonal group O(n)
A recursive method for the construction of irreducible representations of the orthogonal group O(n)
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构造正交群 O(n) 不可约表示的递归方法
DOI：
10.1063/1.532703
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发表时间：
1999
影响因子：
1.3
通讯作者：
N. Barnea
中科院分区：
文献类型：
--
作者：
N. Barnea
提出了一种在不变向量空间中构造O(n)个Gel’fand - zetlin态的算法。这些状态是用一种新的分数父母系数递归地计算出来的。这些系数是格氏不变量的特征向量。结果表明，Gel ' fand不变量矩阵元素的计算可以简化为每一步对单个生成器的求值。该算法为计算正交群的Clebsh-Gordon系数和等标量因子提供了一种新的方法，并且可以应用于构造具有良好定义的正交对称的物理系统的基函数，其中集体运动和与群O(n)相关的固有运动之间的分离是感兴趣的。
An algorithm for the construction of O(n) Gel’fand–Zetlin states in an invariant vector space is developed. The states are calculated recursively using a new type of coefficient of fractional parentage. These coefficients are the eigenvectors of the Gel’fand invariants. It is shown that the calculation of the Gel’fand invariants' matrix elements can be reduced to the evaluation of a single generator at each step. This algorithm provides a new approach to the calculation of the Clebsh–Gordon coefficients and isoscalar factors for the orthogonal group and can be applied to construct a basis function with well-defined orthogonal symmetry for physical systems where separation between collective motions and intrinsic motions, associated with the group O(n), is of interest.