Resumen de Row-column mirror symmetry for colored torus knot homology

Luke Conners

• 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.