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Derived equivalences for symmetric groups and sl(2)-categorification

Abstract:

We define and study sl2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence cate-gorifying the adjoint action of the simple reflection. We construct categorifica-tions for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Broué's abelian defect group conjecture for symmetric groups. We give similar results for gener...

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Publication status:
Published

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Publisher copy:
10.4007/annals.2008.167.245

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ANNALS OF MATHEMATICS
Volume:
167
Issue:
1
Pages:
245-298
Publication date:
2008-01-05
DOI:
ISSN:
0003-486X
URN:
uuid:9430bcf7-f441-4fc2-aec2-3cbc4afd7f71
Source identifiers:
25780
Local pid:
pubs:25780
Language:
English

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