Duality for dormant opers

Abstract

In the present paper, we prove that on a fixed pointed stable curve of characteristic $p>0$, there exists a duality between dormant $\mathfrak{sl}_n$-opers ($1 < n <p-1$) and dormant $\mathfrak{sl}_{(p-n)}$-opers. Also, we prove that there exists a unique (up to isomorphism) dormant $\mathfrak{sl}_{(p-1)}$-oper on a fixed pointed stable curve of characteristic $p>0$.