Stability and disconnected groups

Abstract

We study the notion of semistability for principal bundles over curves with possibly disconnected reductive structure group. We establish a new characterization of the behavior of semistability under change of group, novel even in the connected case, and prove that all existing notions of semistability are equivalent, thus settling a question by Biswas-Gomez. The key ingredients for our results include a study of cocharacters and characters of disconnected linear algebraic groups, and an extension of the recursive description of Kirwan stratifications in Geometric Invariant Theory to the case of disconnected groups.

27 pages, introduction rewritten to better reflect the contents of the paper. Added further exposition