Torus Knots in Adjoint Representation
arXiv:2512.23095 · doi:10.1103/ncsr-z788
Abstract
We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.
typos corrected, refs updated
References in corpus (13)
- Chern-Simons Theory and Topological Strings
- On the Hecke algebras and the colored HOMFLY polynomial
- Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
- On universal knot polynomials
- Universality in Chern-Simons theory
- Nonperturbative universal Chern-Simons theory
- Equations on knot polynomials and 3d/5d duality
- Cabling procedure for the colored HOMFLY polynomials
- On Hopf-induced deformation of topological locus
- Partition function of Chern-Simons theory as renormalized q-dimension
- Macdonald deformation of Vogel's universality and link hyperpolynomials
- Can Yang-Baxter imply Lie algebra?
- Torus knots in adjoint representation and Vogel's universality