Cotangent Models of Nilpotent Orbit Closures

Abstract

Let $\mathcal{O}$ be a nonzero nilpotent orbit in a complex simple Lie algebra $\mathfrak{g}$. For $\mathfrak{g}$ of classical type, we classify the orbit closures $\overline{\mathcal{O}}$ that are isomorphic to $(T^{\ast }X{)}^{\mathrm{aff}}$ for a smooth quasi-affine variety $X$. In types $G_2$, $F_4$, and $E_8$, we show that no nonzero nilpotent orbit closure admits such a cotangent model.

19 pages