Weight conjectures for fusion systems

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 st...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2019-12, Vol.357, p.106825, Article 106825
Hauptverfasser: Kessar, Radha, Linckelmann, Markus, Lynd, Justin, Semeraro, Jason
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2019.106825