q,t-Catalan numbers and knot homology
By E. Gorsky. 2010
64 citations recorded by the source corpus.
We propose an algebraic model of the conjectural triply graded homology of Gukov, Dunfield and Rasmussen for some torus knots. It turns out to be related to the q,t-Catalan numbers of Garsia and Haiman.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6281a735a2271f3d2292063b525061bdc60bd9de
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In Discrete Mathematics and Combinatorics
- B. Eynard
- Alexei Oblomkov
- Vivek V. Shende
- Jacob Rasmussen
- Andrea Brini
- Marcos Mariño
- M. Hedden
- Peter S. Ozsv'ath
In Geometry and Topology
- Marcos Mariño
- B. Eynard
- Alexei Oblomkov
- Vivek V. Shende
- Jacob Rasmussen
- Andrea Brini
- Sergei Gukov
- C. Vafa
In Mathematical Physics
- B. Eynard
- Alexei Oblomkov
- Vivek V. Shende
- Jacob Rasmussen
- Marcos Mariño
- Andrea Brini
- Sergei Gukov
- Peter S. Ozsv'ath
Citations in the corpus
- Torus Knots and Mirror Symmetry (2011, methodology): “As a spinoff of this study, we obtain a formula for the HOMFLY polynomial of a (Q,P ) torus knot in terms of q-hypergeometric polynomials and recover the results of [22].”
- The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link (2012, result): “with one Puiseaux pair to the existing results ([Hag03],[Hag04],[EHKK03]) on the combinatorics of diagonal harmonics and DAHA representations. This connection justifies some of the conjectures made in [Gor10], where a relation between q,t-Catalan numbers and torus knot homology was proposed. As an ou”