Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture

Xiaojun Chen; Weiqiang He; Sirui Yu

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arXiv · 2302.13249

Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture

Xiaojun Chen·Weiqiang He·Sirui Yu

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Abstract

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 [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type.

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BibTeX RIS

Xiaojun Chen, Weiqiang He, Sirui Yu. 2023-02-26. Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture. https://arxiv.org/abs/2302.13249

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