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LetXXbe a compact Riemann surface of genusg≥2g\ge 2,GGbe a semisimple complex Lie group andρ:G→GL(V)\rho :G\to {\rm{GL}}\left(V)be a complex representation ofGG. Given a principalGG-bundleEEoverXX, a vector bundleE(V)E\left(V)whose typical fiber is a copy ofVVis induced. A(G,ρ)\left(G,\rho )-Higgs pair is a pair(E,φ)\left(E,\varphi ), whereEEis a principalGG-bundle overXXandφ\varphiis a holomorphic global section ofE(V)⊗LE\left(V)\otimes L,LLbeing a fixed line bundle overXX. In this work, Higgs pairs of this type are considered forG=Spin(8,C)G={\rm{Spin}}\left(8,{\mathbb{C}})and the three irreducible eight-dimensional complex representations whichSpin(8,C){\rm{Spin}}\left(8,{\mathbb{C}})admits. In particular, the reduced notions of stability, semistability, and polystability for these specific Higgs pairs are given, and it is proved that the corresponding moduli spaces are isomorphic, and a precise expression for the stable and not simple Higgs pairs associated with one of the three announced representations ofSpin(8,C){\rm{Spin}}\left(8,{\mathbb{C}})is described.

Spin(8,C)-Higgs pairs over a compact Riemann surface