论文标题
在对称和交替组的unitriangular基本集
On unitriangular basic sets for symmetric and alternating groups
论文作者
论文摘要
我们研究对称组和交替组的模块化表示理论。在模块化情况下，给定组或代数的不可还原表示的最自然方法之一是显示分解矩阵的unitriangularity，即，即unitriangular碱性集合的存在。我们研究了几种在对称代数的一般情况下获得此类集合的方法。我们将结果应用于对称组及其Hecke代数，从而获得新方法来标记这些对象的简单模块。最后，我们表明，通过研究特征3中的两个显式案例，这些集合并不总是存在于交替组的情况下。
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the decomposition matrices, that is, the existence of a unitriangular basic set. We study several ways to obtain such sets in the general case of a symmetric algebra. We apply our results to the symmetric groups and to their Hecke algebras and thus obtain new ways to label the simple modules for these objects. Finally, we show that these sets do not always exist in the case of the alternating groups by studying two explicit cases in characteristic 3.
