Derived equivalences for symmetric groups and sl2-categorification

By J. Chuang, Raphaël Rouquier. 2004

458 citations recorded by the source corpus.

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

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6a20066e79d6e401db4814d4123100510049585b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A diagrammatic approach to categorification of quantum groups II (2008, unknown): “In his recent talk, R. Rouquier [42] defined sl(N ) and affine sl(N )-categorifications and outlined a conjectural program that aims to vastly generalize his prior work with J. Chuang [9] on sl(2)-categorifications.”
An introduction to diagrammatic algebra and categorified quantum sl(2) (2011, background): “This example was first considered in unpublished work of Khovanov and has since appeared several places in the literature [18, 24].”
A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products (2005, methodology): “The categorification for simple U(sl2)-modules obtained in this way is exactly the one appearing in [CR07].”
Erratum to: Hecke algebras, finite general linear groups, and Heisenberg categorification (2011, methodology): “The analogues of our upward pointing strands were introduced in Chuang-Rouquier [3] in the context of sl2 categorifications in the modular representation theory ofGLn.”