A Cotangent Model for the Next-to-Minimal Orbit of E7

Abstract

Let ${\mathcal{O}}_{2A_1}$ be the next-to-minimal nilpotent orbit of the complex simple Lie algebra of type $E_7$. Let ${\mathfrak{p}}_7$ be the maximal parabolic subalgebra corresponding to the simple root ${\alpha }_7$, and let ${\mathfrak{u}}^{+}$ be its nilpotent radical. We prove that the affinization $T^{\ast }({\mathcal{O}}_{2A_1}\cap {\mathfrak{u}}^{+}{)}^{\mathrm{aff}}$ of the cotangent bundle of ${\mathcal{O}}_{2A_1}\cap {\mathfrak{u}}^{+}$ is isomorphic to the nilpotent orbit closure ${\overline{\mathcal{O}}}_{2A_1}$ as affine varieties.

arXiv comment12 pages