Quantization of the minimal nilpotent orbits and the equivariant Hikita conjecture

Xiaojun Chen, Weiqiang He, Sirui Yu

Published 2023-02-26Version 1

We show that the equivariant cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the $B$-algebra of the quantization of the coordinate ring of the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit,arXiv:1903.12205] and hence verifies the equivariant version of Hikita's conjecture in these cases.