Categorification of the braid groupsReport as inadecuate

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1 IMJ - Institut de Mathématiques de Jussieu

Abstract : 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.

Author: Raphael Rouquier -



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