Weight conjectures for fusion systems
Weight conjectures for fusion systems
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融合系统的重量猜想
DOI：
10.1016/j.aim.2019.106825
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发表时间：
2019
影响因子：
1.7
通讯作者：
Semeraro, Jason
中科院分区：
文献类型：
--
作者：
Kessar, Radha;Linckelmann, Markus;Lynd, Justin;Semeraro, Jason
当前对特征 p 的有限群表示论感兴趣的许多猜想都是局部到全局的陈述，因为它们在给定有关 G 的 p 局部子群表示的数据的情况下预测有限群 G 表示的结果。群代数块的局部结构与 Külshammer-Puig 上同调类的兼容族一起编码在块的融合系统中。受分块理论猜想的启发，我们陈述并启动了对任意三元组（S，F，α）的许多看似局部猜想的研究，该猜想由有限 p 群 S 上的饱和融合系统 F 和兼容族 α 组成。
Many of the conjectures of current interest in the representation theory of finite groups in characteristic p are local-to-global statements, in that they predict consequences for the representations of a finite group G given data about the representations of the p-local subgroups of G. The local structure of a block of a group algebra is encoded in the fusion system of the block together with a compatible family of Külshammer-Puig cohomology classes. Motivated by conjectures in block theory, we state and initiate investigation of a number of seemingly local conjectures for arbitrary triples (S, F, α) consisting of a saturated fusion system F on a finite p-group S and a compatible family α.