Derived equivalences for symmetric groups and 𝔰𝔩2-categorification
نویسندگان
چکیده
منابع مشابه
DERIVED EQUIVALENCES FOR SYMMETRIC GROUPS AND sl2-CATEGORIFICATION
We define and study sl2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications 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 impli...
متن کاملEquivalences of Derived Categories for Symmetric Algebras
It is about a decade since Broué made his celebrated conjecture [2] on equivalences of derived categories in block theory: that the module categories of a block algebra A of a finite group algebra and its Brauer correspondent B should have equivalent derived categories if their defect group is abelian. Since then, character-theoretic evidence for the conjecture has accumulated rapidly, but unti...
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We give a purely geometric categorification of tensor products of finite-dimensional simple Uq(sl2)-modules and R-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification theorems are understood as consequences of Deligne’s theory of weights.
متن کاملDERIVED EQUIVALENCES FOR COTANGENT BUNDLES OF GRASSMANNIANS FROM CATEGORICAL sl2 ACTIONS
We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we answer a question of Namikawa and give an explicit equivalence of categories between coherent sheaves on cotangent bundles to complementary Grassmannians.
متن کاملDERIVED EQUIVALENCES FOR COTANGENT BUNDLES OF GRASSMANNIANS VIA CATEGORICAL sl2 ACTIONS
We construct an equivalence of categories from a strong categorical sl(2) action, following the work of Chuang-Rouquier. As an application, we give an explicit, natural equivalence between the derived categories of coherent sheaves on cotangent bundles to complementary Grassmannians.
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2008
ISSN: 0003-486X
DOI: 10.4007/annals.2008.167.245