Hikita conjecture for the minimal nilpotent orbit

TL;DR

This paper verifies the Hikita conjecture for the minimal nilpotent orbit in simple Lie algebras of type ADE and for the quotient space /, confirming its validity in these specific cases.

Contribution

It provides a proof that the Hikita conjecture holds for the minimal nilpotent orbit of type ADE Lie algebras and for /, expanding the conjecture's verified cases.

Findings

Hikita conjecture verified for minimal nilpotent orbit of type ADE

Confirmed the conjecture for / quotient space

Supports the conjecture's broader applicability

Abstract

We check that the statement of Hikita conjecture holds for the case of the minimal nilpotent orbit of a simple Lie algebra $\mathfrak{g}$ of type ADE and $\mathbb{C} ^2 / \Gamma$.