Rational Cherednik Algebras and Torus Knot Invariants

The HOMFLY polynomial of the $(m,n)$ torus knot Tm,n can be extracted from the doubly graded character of the finite-dimensional representation Lm/n of the type Aₙ₋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 Tm,n by considering a certain filtration on Lm/n. In this paper, we show that two of the proposed candidates, the algebraic filtration and the inductive filtration, are equal.