Mathematics Colloquia and Seminars

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Gorsky-Oblomkov-Rasmusen-Shende observed that the HOMFLY polynomial of the (m, n) torus knot $K_{m,n}$ in the coprime case can be extracted from the doubly graded character of the finite-dimensional representation $L_{m/n}$ of the type $A_{n−1}$ rational Cherednik algebra. They furthermore conjectured that one can obtain the triply-graded Khovanov-Rozansky homology of $K_{m,n}$ by considering certain filtrations on $L_{m/n}$. In this talk, I will introduce two of the proposed candidates, the algebraic filtration and the inductive filtration, and explain why they are equal.