Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions

Abstract

We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra $\mathfrak g$ in terms of the Seifert invariants and standard data for $\mathfrak g$. A main corollary is a determination of the full asymptotic expansions of these invariants for lens spaces in the limit of large quantum level. Our results are in agreement with the asymptotic expansion conjecture due to J. E. Andersen.