# Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology

@article{Evgeny2016FlagHS, title={Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology}, author={Gorsky Evgeny and Negut Andrei and Rasmussen Jacob}, journal={arXiv: Geometric Topology}, year={2016} }

Author(s): Gorsky, Eugene; Neguţ, Andrei; Rasmussen, Jacob | Abstract: We construct a categorification of the maximal commutative subalgebra of the type $A$ Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the (non-symmetric) monoidal category of Soergel bimodules. The adjoint of this functor allows one to match the Hochschild homology of any braid with the Euler characteristic of a sheaf on the…

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#### 33 Citations

Hilbert schemes and $y$-ification of Khovanov-Rozansky homology

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- 2017

Author(s): Gorsky, Eugene; Hogancamp, Matthew | Abstract: We define a deformation of the triply graded Khovanov-Rozansky homology of a link $L$ depending on a choice of parameters $y_c$ for each…

Generalized $q,t$-Catalan numbers

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Author(s): Gorsky, Eugene; Hawkes, Graham; Schilling, Anne; Rainbolt, Julianne | Abstract: Recent work of the first author, Negut and Rasmussen, and of Oblomkov and Rozansky in the context of…

Evaluations of annular Khovanov-Rozansky homology

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Author(s): Gorsky, Eugene; Wedrich, Paul | Abstract: We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal…

Curved Rickard complexes and link homologies

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- 2019

Abstract Rickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we…

Monodromic model for Khovanov-Rozansky homology

- Mathematics
- 2020

We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, in type A, we…

Annular Evaluation and Link Homology

- Mathematics
- 2018

We use categorical annular evaluation to give a uniform construction of both $\mathfrak{sl}_n$ and HOMFLYPT Khovanov-Rozansky link homology, as well as annular versions of these theories. Variations…

Unramified affine Springer fibers and isospectral Hilbert schemes

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- 2018

For any connected reductive group $G$ over $\mathbb{C}$, we revisit Goresky-Kottwitz-MacPherson's description of the torus equivariant Borel-Moore homology of affine Springer fibers…

Moduli Spaces of Sheaves on Surfaces: Hecke Correspondences and Representation Theory

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In modern terms, enumerative geometry is the study of moduli spaces: instead of counting various geometric objects, one describes the set of such objects, which if lucky enough to enjoy good…

Modules over plane curve singularities in any ranks and DAHA

- MathematicsJournal of Algebra
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Abstract We generalize the construction of geometric superpolynomials for unibranch plane curve singularities from our prior paper from rank one to any ranks; explicit formulas are obtained for torus…

3D TQFT and HOMFLYPT homology

- Mathematics, Physics
- 2018

In this note we propose a 3D TQFT such that its Hilbert space on $S^2$, which intersects with defect surfaces along a (possibly self-intersecting) curve $C$ is the HOMFLYPT homology of the link whose…

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