Categorified Young symmetrizers and stable homology of torus links II

• Michael Abel ^[1] ; Matthew Hogancamp ^[2]
  1. [1] Duke University

     Duke University

     Township of Durham, Estados Unidos

     
  2. [2] Indiana University
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 1739-1801
• Idioma: inglés
• DOI: 10.1007/s00029-017-0336-4
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• Resumen

  • We construct complexes P1n of Soergel bimodules which categorify the Young idempotents corresponding to one-column partitions. A beautiful recent conjecture (Flag Hilbert schemes, colored projectors and Khovanov–Rozansky homology.

    arXiv:1608.07308, 2016) of Gorsky–Negut,–Rasmussen relates the Hochschild homology of categorified Young idempotents with the flag Hilbert scheme. We prove this conjecture for P1n 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.