City Research Online

Abstract

Many of the conjectures of current interest in the representation theory of finite groups in characteristic pare local-to-global statements, in that they predict consequencesfor 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 Kulshammer-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.

Publication Type:	Article
Additional Information:	© Elsevier 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Fusion system, Block, Finite group
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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