# A categorification of a cyclotomic Hecke algebra

@article{Oblomkov2018ACO, title={A categorification of a cyclotomic Hecke algebra}, author={Alexei Oblomkov and Lev Rozansky}, journal={arXiv: Representation Theory}, year={2018} }

We propose a categorification of the cyclotomic Hecke algebra in terms of the equivariant K-theory of the framed matrix factorizations. The construction generalizes the earlier construction of the authors for a categorification of the finite Hecke algebra of type A.
We also explain why our construction provides a faithful realization of the Hecke algebras and discuss a geometric realization of the Jucys-Murphy subalgebra.

#### 4 Citations

Notes on Matrix Factorizations and Knot Homology

- Mathematics
- Lecture Notes in Mathematics
- 2019

These are the notes of the lectures delivered by the author at CIME in June 2018. The main purpose of the notes is to provide an overview of the techniques used in the construction of the triply… Expand

Soergel bimodules and matrix factorizations.

- Mathematics, Physics
- 2020

We establish an isomorphism between the Khovanov-Rozansky triply graded link homology and the geometric triply graded homology due to the authors. Hence we provide an interpretation of the… Expand

Dualizable link homology

- Mathematics
- 2019

We modify our previous construction of link homology in order to include a natural duality functor $\mathfrak{F}$.
To a link $L$ we associate a triply-graded module $HXY(L)$ over the graded… Expand

A G ] 2 3 A ug 2 02 1 Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

- 2021

3 Khovanov-Rozansky homology: definitions and computations 6 3.1 Soergel bimodules and Rouquier complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Khovanov-Rozansky homology . . .… Expand

#### References

SHOWING 1-6 OF 6 REFERENCES

IDEMPOTENTS OF HECKE ALGEBRAS OF TYPE A

- Mathematics
- 1997

We use a skein-theoretic version of the Hecke algebras of type A to present three-dimensional diagrammatic views of Gyoja's idempotent elements, based closely on the corresponding Young diagram.
In… Expand

Affine braid group actions on derived categories of Springer resolutions

- Mathematics
- 2011

In this paper we construct and study an action of the affine braid group associated to a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the… Expand

Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology

- Mathematics
- 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… Expand

AFFINE BRAID GROUP, JM ELEMENTS AND KNOT HOMOLOGY

- Mathematics
- 2017

In this paper we construct a homomorphism of the affine braid group Brnaff$$ {\mathfrak{Br}}_n^{\mathrm{aff}} $$ in the convolution algebra of the equivariant matrix factorizations on the space… Expand

Knot homology and sheaves on the Hilbert scheme of points on the plane

- Mathematics
- 2016

For each braid $$\beta \in \mathfrak {Br}_n$$β∈Brn we construct a 2-periodic complex $$\mathbb {S}_\beta $$Sβ of quasi-coherent $$\mathbb {C}^*\times \mathbb {C}^*$$C∗×C∗-equivariant sheaves on the… Expand