Semistability of invariant bundles over $G/\Gamma$

TL;DR

This paper proves that all invariant bundles over the quotient space formed by a connected reductive algebraic group and a cocompact lattice are semistable, contributing to the understanding of bundle stability in algebraic geometry.

Contribution

It establishes the semistability of invariant bundles over quotients of reductive groups by cocompact lattices, a new result in the theory of algebraic bundles.

Findings

Invariant bundles over $G/\Gamma$ are semistable.

The result applies to connected reductive affine algebraic groups.

Provides a foundation for further stability analysis in algebraic geometry.

Abstract

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.