2023/03/28 by Conners, Luke · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2303.16271
We give a recursive construction of the categorified Young symmetrizer introduced by Abel-Hogancamp in arXiv:1510.05330 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-Mellit in arXiv:1909.00418, verifying the mirror symmetry conjectures of arXiv:1112.0030 and arXiv:1304.3481 in this case.