分解有限群的置换表示的一个算法：多项式代数方法
An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra Approach
摘要：
本文描述了一个将特征为零的域上有限群的置换表示分解为不可约部分的算法。该算法是基于这样一个事实，即不变子空间中的不变内积的分量是到这些子空间的投影算子。该算法的一个重要元素是计算多项式理想的Gröbner基。该算法的初步实现将表示拆分为数万个维度。附录中给出了一些计算实例。
英文摘要：
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in invariant subspaces are operators of projection into these subspaces. An important element of the algorithm is the calculation of Gröbner bases of polynomial ideals. A preliminary implementation of the algorithm splits representations up to dimensions of tens of thousands. Some examples of computations are given in appendix.
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