Corpus ID: 125793933

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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References

SHOWING 1-10 OF 41 REFERENCES
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
Author(s): Oblomkov, A; Rasmussen, J; Shende, V; Gorsky, E | Abstract: © 2018, Mathematical Sciences Publishers. All rights reserved. We conjecture an expression for the dimensions of the
Khovanov-Rozansky homology via Cohen-Macaulay approximations and Soergel bimodules
This is the author's diploma thesis. We describe a simplification in the construction of Khovanov-Rozansky's categorification of quantum sl(n) link homology using the theory of maximal Cohen-Macaulay
Hilbert schemes, polygraphs and the Macdonald positivity conjecture
We study the isospectral Hilbert scheme X_n, defined as the reduced fiber product of C^2n with the Hilbert scheme H_n of points in the plane, over the symmetric power S^n C^2. We prove that X_n is
Torus knots and the rational DAHA
Author(s): Gorsky, E; Oblomkov, A; Rasmussen, J; Shende, V | Abstract: © 2014. We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m;n) torus knot from the unique
Triply-graded link homology and Hochschild homology of Soergel bimodules
We consider a class of bimodules over polynomial algebras which were originally introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct summand of the category of
Categorified Young symmetrizers and stable homology of torus links
We construct complexes $P_{1^n}$ of Soergel bimodules which categorify the Young idempotents corresponding to one-column partitions. A beautiful recent conjecture of Gorsky-Rasmussen relates the
A polynomial action on colored sl(2) link homology
We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is
The Superpolynomial for Knot Homologies
TLDR
A framework for unifying the sl(N) Khovanov– Rozansky homology with the knot Floer homology is proposed, and a rich formal structure is proposed that is powerful enough to make many nontrivial predictions about the existing knot homologies that can then be checked directly.
Stable homology of torus links via categorified Young symmetrizers I: one-row partitions
We show that the triply graded Khovanov-Rozansky homology of the torus link $T_{n,k}$ stablizes as $k\to \infty$. We explicitly compute the stable homology (as a ring), which proves a conjecture of
Jones polynomials of torus knots via DAHA
We suggest a construction for the Quantum Groups–Jones polynomials of torus knots in terms of the PBW theorem of double affine Hecke algebra (DAHA) for any root systems and weights (justified for
...
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