Torus knots and the rational DAHA

@article{Gorsky2014TorusKA,
  title={Torus knots and the rational DAHA},
  author={Eugene Gorsky and Alexei Oblomkov and Jacob Rasmussen and Vivek V. Shende},
  journal={Duke Mathematical Journal},
  year={2014},
  volume={163},
  pages={2709-2794}
}
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 finite-dimensional simple representation of the rational DAHA of type A, rank n - 1, and central character m/n. The conjectural differentials of Gukov, Dunfield, and the third author receive an explicit algebraic expression in this picture, yielding a prescription for the doubly graded Khovanov-Rozansky… Expand

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  • A. T. Wilson
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 2018
TLDR
A combinatorial formula for the homologies of all links considered by Elias and Hogancamp and conjecture a direct relationship between the $(n,n)$ torus link case of the formula and the symmetric function $\nabla p_{1^n}$. Expand
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