On Hecke lifting conjecture for framed knots
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917022113202176 |
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| author | Zhu, Shengmao |
| author_facet | Zhu, Shengmao |
| contents | Motivated by an amazing integrality structure conjecture for the $U(N)$ Chern-Simons quantum invariants of framed knots investigated by Mariño and Vafa, a new conjectural formula, named Hecke lifting conjecture, was proposed in \cite{CLPZ23} for framed links. This note is devoted to the study of this Hecke lifting conjecture. We prove this conjecture for torus knots using the explicit formulas of colored HOMFLY-PT invariants of torus knots, and we also verify the conjecture in a limit form for any framed knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hecke lifting conjecture for framed knots Zhu, Shengmao Geometric Topology High Energy Physics - Theory Motivated by an amazing integrality structure conjecture for the $U(N)$ Chern-Simons quantum invariants of framed knots investigated by Mariño and Vafa, a new conjectural formula, named Hecke lifting conjecture, was proposed in \cite{CLPZ23} for framed links. This note is devoted to the study of this Hecke lifting conjecture. We prove this conjecture for torus knots using the explicit formulas of colored HOMFLY-PT invariants of torus knots, and we also verify the conjecture in a limit form for any framed knots. |
| title | On Hecke lifting conjecture for framed knots |
| topic | Geometric Topology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.15692 |