A note on the bundle underlying Opers

Abstract

In this note we write down a proof of the following well known fact, in order to make the literature more transparent. Let $\mathfrak{g}$ be a simple Lie algebra, then for any smooth curve $C$, the bundle underlying any $\mathfrak{g}$-Oper depends only on the curve and it is induced by the canonical $\text{Aut}\, O$ bundle $\text{Aut}_C$ on $C$.