论文标题
有限群体和谎言理论的模块化表示
Modular representations of finite groups and Lie theory
论文作者
论文摘要
本文从布鲁伊的阿贝尔缺陷组猜想的角度讨论了有限的谎言类型群体的模块化表示理论。 我们既讨论了定义的特征案例，阿尔珀林重量猜想的灵感，也讨论了非定义的案例，这是布鲁伊猜想的灵感。一般有限基团的模块化表示理论被认为是在很大程度上定义特征和非定义特征的有限型群体类型的行为。 定义特征有限群体类型的有限群体的模块化表示理论的预期行为尤其难以掌握Broue的猜想的线条，我们提出了一个与中心特征变化有关的新问题。 我们在非定义特征的谎言类型有限群的模块化表示理论中介绍了一种变性方法。结合不正确等效的刚度属性，这为两个可变分解矩阵提供了一个设置，以实现大型特征。这应该有助于在寻找分解矩阵方面取得进展，这是一个杰出的问题，除了一般线性群体外，很少有一般结果。最后一部分是基于与David Craven和Olivier Dudas的共同合作。
This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broue's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight conjecture, and the non-defining case, the inspiration for Broue's conjecture. The modular representation theory of general finite groups is conjectured to behave both like that of finite groups of Lie type in defining characteristic, and in non-defining characteristic, to a large extent. The expected behaviour of modular representation theory of finite groups of Lie type in defining characteristic is particularly difficult to grasp along the lines of Broue's conjecture and we raise a new question related to the change of central character. We introduce a degeneration method in the modular representation theory of finite groups of Lie type in non-defining characteristic. Combined with the rigidity property of perverse equivalences, this provides a setting for two variable decomposition matrices, for large characteristic. This should help make progress towards finding decomposition matrices, an outstanding problem with few general results beyond the case of general linear groups. This last part is based on joint work with David Craven and Olivier Dudas.
