Categorification of the braid groups
By Raphaël Rouquier. 2004
76 citations recorded by the source corpus.
We construct a categorification of the braid groups associated with Coxeter groups inside the homotopy category of Soergel's bimodules. Classical actions of braid groups on triangulated categories should come from an action of this monoidal category. We construct representations of this monoidal category on category O of a complex semi-simple Lie algebra and on constructible sheaves over flag varieties. We also consider general constructions of self-equivalences as reflections around another category.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2262412600036b5425578cbaeb1e7780e3599456
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In Geometry and Topology
- Eric Zaslow
- D. Nadler
- Christopher Brav
- Hugh Thomas
- David Treumann
- Chiu-Chu Melissa Liu
- Bohan Fang
- St'ephane Guillermou
In Mathematical Physics
- Eric Zaslow
- D. Nadler
- Christopher Brav
- Hugh Thomas
- David Treumann
- Chiu-Chu Melissa Liu
- Bohan Fang
- St'ephane Guillermou
Citations in the corpus
- Braid groups and Kleinian singularities (2009, background): “We begin by reviewing some aspects of the theory of spherical objects (introduced in [14] and refined in [13] and [1]).”
- Constructible sheaves and the Fukaya category (2006, background): “Namely, under the embedding of this paper, the kernels giving the usual braid group action on the constructible derived category Dc(B) (see for example Rouquier [31]) induce a corresponding action on DFuk(T ∗B).”