We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov to appear in Proc. Amer. Math. Soc. and hence verifies in this case the quantum version of Hikita’s conjecture, proposed by Kamnitzer, McBreen and Proudfoot Adv. Math. 390 (2021). As a corollary, we get the Hikita-Nakajima conjecture in this case. We also show analogous isomorphisms for singularities of BCFG type.
Chen et al. (Fri,) studied this question.