Automorphisms of the moduli space of principal $G$-bundles induced by outer automorphisms of $G$

Abstract

In this work we study finite-order automorphisms of the moduli space of principal $G$-bundles coming from outer automorphisms of the structure group when $G$ is a simple complex Lie group. We do this by describing the subvarieties of fixed points for the action of that automorphisms on the moduli space of principal $G$-bundles. In particular, we prove that these fixed points are reductions of structure group to the subgroup of fixed points of the outer automorphism. Moreover, we study the way in which these fixed points fall into the stable or nonstable locus of the moduli.