Reshetikhin-Turaev construction and $\mathrm{U}(1)^n$ Chern-Simons partition function

In this article, we show that the $\mathrm{U}(1)^n$ Chern-Simons partition functions are related to Reshetikhin-Turaev invariants. In this abelian context, it turns out that the Reshetikhin-Turaev construction that yields these invariants relies on a ``twisted" category rather than a modular one. Furthermore, the Chern-Simons duality of the $\mathrm{U}(1)^n$ partition functions straightforwardly extend to the corresponding Reshetikhin-Turaev invariants.