Reversible Higgs Bundles

We study reversible Higgs bundles on a compact Riemann surface $Σ$ of genus $g\geq 2$, that is, $G$-Higgs bundles $(E,Φ)$ with $(E,Φ)\cong(E,-Φ)$. For a complex reductive group $G$ realized as a self-adjoint subgroup of $GL(n,\mathbb{C})$, we show that if $(E,Φ)$ corresponds to a representation $ρ$