Row-Column Mirror Symmetry for Colored Torus Knot Homology
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910529825538048 |
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| author | Conners, Luke |
| author_facet | Conners, Luke |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16271 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Row-Column Mirror Symmetry for Colored Torus Knot Homology Conners, Luke Geometric Topology Quantum Algebra Representation Theory 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. |
| title | Row-Column Mirror Symmetry for Colored Torus Knot Homology |
| topic | Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2303.16271 |