# Categorification of the braid groups

@article{Rouquier2004CategorificationOT, title={Categorification of the braid groups}, author={Raphael Rouquier}, journal={arXiv: Representation Theory}, year={2004} }

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…

## 68 Citations

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- Mathematics
- 2006

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- MathematicsCompositio Mathematica
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Abstract We construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel–Thomas) twists…

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### A Diagrammatic Temperley-Lieb Categorification

- MathematicsInt. J. Math. Math. Sci.
- 2010

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We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical…

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