Mukai-Sakai bound for equivariant principal bundles

Abstract

Mukai and Sakai proved that given a vector bundle E of rank n on a connected smooth projective curve of genus g and any r∈[1, n], there is subbundle S of rank r such that deg Hom(S, E/S)≤r(n−r)g. We prove a generalization of this bound for equivariant principal bundles. Our proof even simplifies the one given by Holla and Narasimhan for usual principal bundles.