Aut(W)-invariant Landau–Ginzburg/Calabi–Yau correspondence

Assume $W$ satisfies the Calabi–Yau condition and $G$ is a subgroup with $\langle j_W\rangle\subseteq G\subseteq\operatorname{Aut}(W)$. Consider the $\operatorname{Aut}(W)$-invariant parts of the FJRW and Chen–Ruan theories on the two sides. Aut(W)-invariant LG–CY correspondence. The Landau–Ginzburg/Calabi–Yau correspondence holds for the $\operatorname{Aut}(W)$-invariant theories on both sides. The source states that the preceding conjecture was proved in genus zero for the quintic threefold and for Fermat hypersurfaces with $G=\langle j\rangle$, but does not claim an all-genus proof of this invariant specialization.