F 4 and PSp (8, ℂ)-Higgs pairs understood as fixed points of the moduli space of E 6-Higgs bundles over a compact Riemann surface

Abstract Let X X be a compact Riemann surface of genus g ≥ 2 g 2 and ℳ (E 6) { M } (E₆) be the moduli space of E 6 E₆ -Higgs bundles over X X. We consider the automorphisms σ + + of ℳ (E 6) { M } (E₆) defined by σ + (E, φ) = (E ∗, − φ t) + (E, ) = (E^, - ^t), induced by the action of the outer involution of E 6 E₆ in ℳ (E 6) <jat