Normality of orthogonal and symplectic nilpotent orbit closures in positive characteristic (Q497700)

Let \(G=O(V)\) or \(\mathrm{Sp}(V)\) be the orthogonal or symplectic group over an algebraically closed field of prime characteristic, and \(\mathfrak{g}=\text{Lie}(G)\). Let \(\mathcal{O}\) be a nilpotent \(G\)-orbit in \(\mathfrak{g}\). In this paper, the authors provide a sufficient condition and a necessary condition for the Zariski closure \(\overline{\mathcal{O}}\) of \(\mathcal{O}\) to be normal. More precise, the authors show that (1) \(\overline{\mathcal{O}}\) is normal provided that neither type \(d\) nor type \(e\) minimal irreducible degeneration occurs in \(\overline{\mathcal{O}}\); (2) the normal property of \(\overline{\mathcal{O}}\) implies that any type \(e\) minimal irreducible degeneration does not occur in \(\overline{\mathcal{O}}\).