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We give a recursive construction of the categorified Young symmetrizerintroduced by Abel-Hogancamp in arXiv:1510.05330 corresponding to thesingle-column partition. As a consequence, we obtain new expressions for theuncolored $y$-ified HOMFLYPT homology of positive torus links and the $y$-ifiedcolumn-colored HOMFLYPT homology of positive torus knots. In the latter case,we compare with the row-colored homology of positive torus knots computed byHogancamp-Mellit in arXiv:1909.00418, verifying the mirror symmetry conjecturesof arXiv:1112.0030 and arXiv:1304.3481 in this case.

Row-Column Mirror Symmetry for Colored Torus Knot Homology