TY - JOUR
T1 - Torus knots and the rational DAHA
AU - Gorsky, Eugene
AU - Oblomkov, Alexei
AU - Rasmussen, Jacob
AU - Shende, Vivek
N1 - Publisher Copyright:
© 2014.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2827126
DO - 10.1215/00127094-2827126
M3 - Article
AN - SCOPUS:84920085189
SN - 0012-7094
VL - 163
SP - 2709
EP - 2794
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 14
ER -