Higgs bundles for real groups and the Hitchin-Kostant-Rallis section - García-Prada, Oscar; Peón-Nieto, Ana; Ramanan, Sundararaman (Transactions of the American Mathematical Society, 2018)
We consider the moduli space of polystable-twisted-Higgs bundles over a compact Riemann surface, where is a real reductive Lie group and is a holomorphic line bundle over. Evaluating the Higgs field on a basis of the ring of polynomial invariants of the isotropy representation defines the Hitchin map.