Lee filtration structure of torus links

We determine the quantum filtration structure of the Lee homology of all torus links. In particular, this determines the \(s\)-invariant of a torus link equipped with any orientation. In the special case \(T(n,n)\), our result confirms a conjecture of Pardon, as well as a conjecture of Manolescu-Marengon-Sarkar-Willis which establishes an adjunction-type inequality of the \(s\)-invariant for cobordisms in \(k\overline{\mathbb{CP}^2}\). We also give a few applications of this adjunction inequality.