Categorified skew Howe duality and comparison of knot homologies

@article{Mackaay2015CategorifiedSH,
  title={Categorified skew Howe duality and comparison of knot homologies},
  author={M. Mackaay and B. Webster},
  journal={arXiv: Geometric Topology},
  year={2015}
}
In this paper, we show an isomorphism of homological knot invariants categorifying the Reshetikhin-Turaev invariants for $\mathfrak{sl}_n$. Over the past decade, such invariants have been constructed in a variety of different ways, using matrix factorizations, category $\mathcal{O}$, affine Grassmannians, and diagrammatic categorifications of tensor products. While the definitions of these theories are quite different, there is a key commonality between them which makes it possible to prove… Expand
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