On Quantization of a Nilpotent Orbit Closure in $G_2$

TL;DR

This paper constructs a quantization model for the non-normal orbit closure in the Lie algebra of the exceptional group G2, confirming a long-standing conjecture by Vogan from 1984.

Contribution

It provides the first explicit quantization of the non-normal orbit closure in G2, verifying Vogan's conjecture from 1984.

Findings

Quantization model for the non-normal orbit closure in G2

Verification of Vogan's conjecture from 1984

Explicit description of the orbit closure's quantization

Abstract

Let $G$ be the complex exceptional Lie group of type $G_2$. Among the five nilpotent orbits in its Lie algebra $\mathfrak{g}$, only the 8-dimensional orbit $\mathcal{O}_8$ has non-normal orbit closure $\bar{\mathcal{O}_8}$. In this short note, we will give a quantization model of $\bar{\mathcal{O}_8}$, verifying a conjecture of Vogan in 1984.