All Questions

$\DeclareMathOperator\SO{SO}\DeclareMathOperator\SL{SL}\DeclareMathOperator\GL{GL}$Let $X$ be a compact Riemann surface. Let $G$ be a real reductive Lie group, $H$ be a maximal compact subgroup of $G$ ...

I'm reading the Bruzzo and Graña Otero's paper Semistable and Numerically Effective Principal (Higgs) Bundles; here: $X$ is a smooth, complex, projective variety; $G$ is a connected, complex, ...