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Categorified Young symmetrizers and stable homology of torus links II (1510.05330v2)
Published 19 Oct 2015 in math.QA and math.GT
Abstract: We construct complexes $P_{1n}$ 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 $P_{1n}$ 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.