  We construct complexes $P_{1^n}$ of Soergel bimodules which categorify the
Young idempotents corresponding to one-column partitions. A beautiful recent
conjecture of Gorsky-Rasmussen relates the Hochschild homology of categorified
Young idempotents with the flag Hilbert scheme. We prove this conjecture for
$P_{1^n}$ and its twisted variants. We also show that this homology is also a
certain limit of Khovanov-Rozansky homologies of torus links. Along the way we
obtain several combinatorial results which could be of independent interest.
