https://doi.org/10.1140/epjc/s10052-025-14651-7
Regular Article - Theoretical Physics
Torus knots in adjoint representation and Vogel’s universality
1
Lebedev Physics Institute, 119991, Moscow, Russia
2
Institute for Information Transmission Problems, 127994, Moscow, Russia
3
NRC “Kurchatov Institute”, 123182, Moscow, Russia
Received:
1
July
2025
Accepted:
12
August
2025
Published online:
28
August
2025
Vogel’s universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters 
, which are homogeneous coordinates of Vogel’s plane. It is associated with representation theory within the framework of Chern–Simons theory only, and gives rise to universal knot invariants. We extend the list of these latter further, and explain how to deal with the adjoint invariants for the torus knots T[m, n] considering the case of T[4, n] with odd n in detail.
© The Author(s) 2025
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