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The HOMFLY polynomial of the (m, n) torus knot T₌, ₍ can be extracted from the doubly graded character of the finite-dimensional representation L₌₍ of the type A₍-₁ rational Cherednik algebra as observed by Gorsky, Oblomkov, Rasmussen and Shende. It is furthermore conjectured that one can obtain the triply-graded Khovanov-Rozansky homology of T₌, ₍ by considering a certain filtration on L₌₍. In this paper, we show that two of the proposed candidates, the algebraic filtration and the inductive filtration, are equal.
Xinchun Ma (Wed,) studied this question.