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Beyond Broué's conjecture

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GR2W01 - Counting conjectures and beyond

Broué’s abelian defect group conjecture gives a prediction for the derived category of blocks with abelian defect groups. While the derived category encodes the number of simple modules, it does not determine decomposition matrices.  I will discuss how Broue’s conjecture can be used nevertheless to make predictions about decomposition matrices of finite groups of Lie type in non-describing characteristic. A key role is played by perverse equivalences, which provide additional information. The actual combinatorics of “generic” decomposition matrices should stem from the presence of certain double gradings. (based on joint work with David Craven and Olivier Dudas).

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

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