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
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• 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.