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Categorification of the braid groups
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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.
Forward citations
Cited by 2 Pith papers
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Stable deformed $\mathfrak{gl}_N$ homology of torus knots
The authors compute the E2 page of the Rasmussen spectral sequence for stable gl_N Khovanov-Rozansky homology of torus knots, verifying the predicted algebraic description for all N.
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The Last Three T-degrees in Triply-Graded Link Homology
For any braid, the outermost three T-degree layers of reduced triply-graded HOMFLY homology are determined explicitly, and are almost entirely zero with only a few one-dimensional k-modules.
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