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Counting conjectures for fusion systems

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GR2W01 - Counting conjectures and beyond

An ℓ-compact group is a homotopical analogue of a compact Lie group whose homotopy fixed point spaces are classifying spaces of fusion systems of finite groups of Lie type. After motivating the study of weights for fusion systems, I will report on the first part of ongoing joint work with Gunter Malle and Radha Kessar investigating weights associated to homotopy fixed point spaces of ℓ-compact groups. We showed that certain equations predicted by local-global conjectures in the modular representation theory of finite groups of Lie type continue to hold in the ℓ-compact setting. If time permits, I will show these equations hold even more generally in the category of ℓ-local compact groups, pointing towards some yet unknown structural explanation for them purely in the framework of fusion systems.

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

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