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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