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Reduction Theorems for Generalised Block Fusion Systems

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GRA2 - Groups, representations and applications: new perspectives

One of the main problems in the theory of fusion systems is the conjecture whether a fusion system arises in the form of a finite group if and only if it arises in the form of a p-block of a finite group. A category, called generalised block fusion systems, plays an important role in reduction theorems related to this conjecture. We generalise several key results for block fusion systems to generalised block fusion systems and apply one of these results to extend a theorem by Cabanes about the non-exoticity of fusion systems of unipotent blocks and discuss our strategy to prove the conjecture for fusion systems of blocks of finite groups of Lie type.

This talk is part of the Isaac Newton Institute Seminar Series series.

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