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We show that the specialized quantum D-module of the equivariant quantumcohomology ring of the minimal resolution of an ADE singularity is isomorphicto the D-module of graded traces on the minimal nilpotent orbit in the Liealgebra of the same type. This generalizes a recent result of Shlykov [Hikitaconjecture for the minimal nilpotent orbit, to appear in Proc. AMS,https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantumversion of Hikita's conjecture, proposed by Kamnizter, McBreen and Proudfoot[The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. Wealso show analogous isomorphisms for singularities of BCFG type.

Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture