On the Bieri-Neumann-Strebel-Renz invariants and limit groups over Droms RAAGs

For a group $G$ that is a limit group over Droms RAAGs such that $G$ has trivial center, we show that $Sigma^1(G) = emptyset = Sigma^1(G, mathbb{Q})$. For a group $H$ that is a finitely presented residually Droms RAAG we calculate $Sigma^1(H)$ and $Sigma^2(H)_{dis}$. In addition, we obtain a necessary condition for $[chi]$ to belong to $Sigma^n(H)$.