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

Abstract Let X X be a compact Riemann surface of genus g ≥ 2 g\ge 2 and ℳ ( E 6 ) {\mathcal{ {\mathcal M} }}\left({E}_{6}) the moduli space {E}_{6} -Higgs bundles over . We consider automorphisms σ + {\sigma }_{+} defined by , φ = ∗ − t }_{+}\left(E,\varphi )=\left({E}^{\ast },-{\varphi }^{t}) , induced action outer involution in }_{-} }_{-}\left(E,\varphi },{\varphi which results from combination with consists on change sign Higgs field. In this work, we describe fixed points as F 4 {F}_{4} bundles, pairs associated fundamental irreducible representation mathvariant="normal">PSp 8 mathvariant="double-struck">C {\rm{PSp}}\left(8,{\mathbb{C}}) second symmetric power or wedge mathvariant="normal">Sp {\rm{Sp}}\left(8,{\mathbb{C}}) Finally, reduced notions semistability polystability for these objects.