https://doi.org/10.1140/epjc/s10052-025-15222-6
Regular Article - Theoretical Physics
On Hecke lifting conjecture for framed knots
Department of mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, China
a
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Received:
29
October
2025
Accepted:
16
December
2025
Published online:
29
December
2025
Abstract
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 Chen et al. (Commun Math Phys 400:683–729, 2023) 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.
© The Author(s) 2025
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