Invariant vector bundles and Hitchin systems

Abstract

Let $X\to Y$ be a Galois cover with Galois group Γ, where X and Y are smooth complex projective curve of genus ⩾2. In this paper, we study the moduli spaces of semistable Γ-invariant vector bundles on X and classify their connected components. We also study the Hitchin systems on these moduli spaces and determine their fibers in the smooth case.