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arXiv · 1510.05330

Categorified Young symmetrizers and stable homology of torus links II

Michael Abel·Matthew Hogancamp
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Abstract

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.

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Michael Abel, Matthew Hogancamp. 2016-02-02. Categorified Young symmetrizers and stable homology of torus links II. https://arxiv.org/abs/1510.05330

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