Large- N torus knots in lens spaces and their quiver structure

We study colored Hoste, Ocneanu, Millett, Freyd, Lickorish, Yetter, Przytycki, and Traczyk invariants of torus knots in the lens space S3/Zp within U(N) Chern–Simons (CS) theory. Using the surgery and modular description of lens spaces, we derive a general expression for the invariant of an (α, β) torus knot in this background. In the large-N limit these invariants simplify and acquire a universal form: the invariant of an (α, β) torus knot in S3/Zp can be expressed in terms of the invariant of the (α, α + pβ) torus knot in S3. After an appropriate redefinition of knot variables, the generating functions of these invariants exhibit a structure analogous to quiver partition functions. Since the associated quiver is independent of the rank N and level k of CS theory, the large-N result provides a direct way to identify the underlying quiver, allowing us to determine the quiver structure associated with torus knots in S3/Zp.