Gorsky–Oblomkov–Rasmussen filtration conjecture for rational Cherednik representations

Let $m,n$ be coprime positive integers, let $\mathfrak{h}$ be the $(n-1)$-dimensional standard representation of $S_n$, and let $\mathrm{L}_{\frac{m}{n}}$ be the unique finite-dimensional irreducible representation of the rational Cherednik algebra $\mathrm{H}_{\frac{m}{n}}$. Write $T_{m,n}$ for the $(m,n)$ torus knot and let $\mathrm{H}\mathrm{H}\mathrm{H}(T_{m,n})$ denote its triply graded Khovanov–Rozansky homology. The hook-isotypic components are $\operatorname{Hom}_{S_n}(\wedge^i(\mathfrak{h}),\mathrm{L}_{\frac{m}{n}})$. Gorsky–Oblomkov–Rasmussen conjecture. There exists a filtration on $\mathrm{L}_{\frac{m}{n}}$ whose associated $t$-grading refines the HOMFLY identity to

$$\mathrm{ch}_{a,q,t}(\mathrm{H}\mathrm{H}\mathrm{H}(T_{m,n}))=a^{(n-1)(m-1)}\sum_{i=0}^{n-1}a^{2i}\mathrm{ch}_{q,t}\bigl(\operatorname{Hom}_{S_n}(\wedge^i(\mathfrak{h}),\mathrm{L}_{\frac{m}{n}})\bigr).$$

The conjecture proposes a representation-theoretic realization of the third homological grading of torus-knot Khovanov–Rozansky homology; the supplied text gives no resolution status.