Irreducible restrictions of representations of symmetric and alternating groups in small characteristics
Irreducible restrictions of representations of symmetric and alternating groups in small characteristics
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小特征中对称群和交替群表示的不可约限制
DOI：
10.1016/j.aim.2020.107184
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发表时间：
2020
影响因子：
1.7
通讯作者：
Tiep, Pham Huu
中科院分区：
文献类型：
--
作者：
Kleshchev, Alexander;Morotti, Lucia;Tiep, Pham Huu
建立在我们以前的工作中得到的对称群的约化定理和维数界，我们分类的对称和交替群的表示的不可约的限制，以适当的子群。当地面场的特征大于3时，这样的分类是已知的，但是小特征的情况需要更加精细的分析和新的想法。我们的结果符合Aschbacher-Scott关于有限典型群的极大子群的程序。
Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such a classification is known when the characteristic of the ground field is greater than 3, but the small characteristics cases require a substantially more delicate analysis and new ideas. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.