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Row-column mirror symmetry for colored torus knot homology

  • Luke Conners [1]
    1. [1] Department of Mathematics, University of North Carolina. USA
  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
  • Idioma: inglés
  • DOI: 10.1007/s00029-024-00984-w
  • Enlaces
  • Resumen

    • We give a recursive construction of the categorified Young symmetrizer introduced by Abel and Hogancamp (Sel Math (NS) 23:1739–1801, 2017) corresponding to the single-column partition. As a consequence, we obtain new expressions for the uncolored y-ified HOMFLYPT homology of positive torus links and the y-ified column-colored HOMFLYPT homology of positive torus knots. In the latter case, we compare with the row-colored homology of positive torus knots computed by Hogancamp and Mellit (Torus link homology, 2019), verifying the mirror symmetry conjectures of Gukov and Stošić (Geom Topol Monogr 18:309–367, 2012) and Gorsky et al. (Fund Math 243:209–299, 2018) in this case.

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