Torus knots and the rational DAHA

Eugene Gorsky, Alexei Oblomkov, Jacob Rasmussen, Vivek Shende

Research output: Contribution to journalArticlepeer-review

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 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 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.

Original languageEnglish (US)
Pages (from-to)2709-2794
Number of pages86
JournalDuke Mathematical Journal
Volume163
Issue number14
DOIs
StatePublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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