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arXiv · 2608.12985

Minimal Nilpotent Orbits of type G2, F4 and E8

Boming Jia
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Abstract

Let $\mathfrak g$ be a complex simple Lie algebra of type $G_2$, $F_4$, or $E_8$. We prove that the closure $\overline{\mathcal O}_{\min}(\mathfrak g)$ of its minimal nilpotent orbit is not isomorphic to $(T^*X)^{\mathrm{aff}}$ for any smooth quasi-affine variety $X$. We do not assume that the isomorphism is equivariant or Poisson. We also prove the same statement in types $A_1$ and $A_2$.

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Boming Jia. 2026-08-13. Minimal Nilpotent Orbits of type G2, F4 and E8. https://arxiv.org/abs/2608.12985

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