论文标题
有限组的分解线性表示
Decomposing Linear Representations of Finite Groups
论文作者
论文摘要
我们使用计算机代数系统差距开发一个软件包，以计算有限的组$ g $的表示$ \ mathbb {c} $的分解为norreDucibles，以及$ρ（g）$的Centraliser Ring的相应分解。当前，用于分解表示形式的唯一开源程序是针对非零特征字段。尽管已知特征零的方法，但没有开源计算机程序可以实施这些方法，也没有有关如何实现此类实现的良好性能的详细信息。我们旨在记录此类细节并演示我们计划在减少半菲尼特程序规模时的应用。
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $ρ$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser ring of $ρ(G)$. Currently, the only open-source programs for decomposing representations are for non-zero characteristic fields. While methods for characteristic zero are known, there are no open-source computer programs that implement these methods, nor are details on how to achieve good performance of such an implementation published. We aim to record such details and demonstrate an application of our program in reducing the size of semidefinite programs.
