Year: 2014
Type: article
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.
Source: Duke Mathematical Journal
Authors: Eugene Gorsky, Alexei Oblomkov, Jacob Rasmussen, Vivek Shende
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2057376802