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SUMMARY:Beyond Broué's conjecture - Raphael Rouquier (University of Calif
 ornia\, Los Angeles)
DTSTART:20220509T123000Z
DTEND:20220509T132000Z
UID:TALK172769@talks.cam.ac.uk
DESCRIPTION:Brou&eacute\;'s abelian defect group conjecture gives a predic
 tion for the&nbsp\;derived category of blocks with abelian defect groups. 
 While the derived category encodes the number of simple modules\, it does 
 not&nbsp\;determine decomposition matrices.&nbsp\;\nI will discuss how Bro
 ue's conjecture can be used nevertheless to make predictions about decompo
 sition matrices of finite groups of Lie type in non-describing characteris
 tic. A key role is played by perverse equivalences\, which provide additio
 nal information. The actual combinatorics of "generic" decomposition matri
 ces should stem from the presence of certain double gradings.\n(based on j
 oint work with David Craven and Olivier Dudas).
LOCATION:Seminar Room 1\, Newton Institute
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