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Weight conjectures for fusion systems

Kessar, R. ORCID: 0000-0002-1893-4237, Linckelmann, M., Lynd, J. and Semeraro, J. (2019). Weight conjectures for fusion systems. Advances in Mathematics, 357, 106825.. doi: 10.1016/j.aim.2019.106825

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 Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/22882
[img] Text - Accepted Version
This document is not freely accessible until 30 September 2020 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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