Translator Disclaimer
1 November 2014 Torus knots and the rational DAHA
Eugene Gorsky, Alexei Oblomkov, Jacob Rasmussen, Vivek Shende
Duke Math. J. 163(14): 2709-2794 (1 November 2014). DOI: 10.1215/00127094-2827126

Abstract

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 n1, 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 homologies. We match our conjecture to previous conjectures of the first author relating knot homology to q,t-Catalan numbers and to previous conjectures of the last three authors relating knot homology to Hilbert schemes on singular curves.

Citation

Download Citation

Eugene Gorsky. Alexei Oblomkov. Jacob Rasmussen. Vivek Shende. "Torus knots and the rational DAHA." Duke Math. J. 163 (14) 2709 - 2794, 1 November 2014. https://doi.org/10.1215/00127094-2827126

Information

Published: 1 November 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1318.57010
MathSciNet: MR3273582
Digital Object Identifier: 10.1215/00127094-2827126

Subjects:
Primary: 57M25
Secondary: 05A99, 14H20, 16G99

Rights: Copyright © 2014 Duke University Press

JOURNAL ARTICLE
86 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.163 • No. 14 • 1 November 2014
Back to Top