HOMFLYPT homology of Coxeter links

A Coxeter link is a closure of a product of two braids, one being a quasi-Coxeter element and the other being a product of partial full twists. This class of links includes torus knots $T_{n,k}$ and torus links $T_{n,nk}$. We identify the knot homology of a Coxeter link with the space of sections of a particular line bundle on a natural generalization of the punctual locus inside the flag Hilbert scheme of points in $\mathbb{C}^2$.