论文标题
在字符表上查找过渡剂理论
Finding Supercharacter Theories on Character Tables
论文作者
论文摘要
我们描述了一种简单的方法，如果知道其字符表，则如何找到有限群体的增压理论。也就是说，我们展示了如何将共轭类别或不可约特征的任意分区改进到属于增压器理论的最粗糙分区。我们的构造强调了超类和增压器之间的二元性。提出了一种算法，以在给定的字符表上找到所有的增压器理论。该算法用于计算某些具有多达26个共轭类的非亚伯简单组的增压特性理论数量。
We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show how an arbitrary partition of the conjugacy classes or of the irreducible characters can be refined to the coarsest partition that belongs to a supercharacter theory. Our constructions emphasize the duality between superclasses and supercharacters. An algorithm is presented to find all supercharacter theories on a given character table. The algorithm is used to compute the number of supercharacter theories for some nonabelian simple groups with up to 26 conjugacy classes.
