Semistability of invariant bundles over $G/\Gamma$
  Let $G$ be a connected reductive affine algebraic group defined over $\mathbb C$, and let $\Gamma$ be a cocompact lattice in $G$. We prove that any invariant bundle on $G/\Gamma$ is semistable. 
Indranil Biswas
math.DG math.AG