2025/10/17 by Shengmao Zhu, Zhu, Shengmao
Mathematics · #Geometric and Algebraic Topology #Algebraic structures and combinatorial models #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2510.15692
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 \citeCLPZ23 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.