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New Exotic Pieces of the Character Variety of Surface Groups in the Group G₂′

November 13, 2026arXiv: 2611.14503v1

A recent study finds connected components of representations of a surface group in the exceptional Lie group G₂′ that are neither deformations of the usual Fuchsian representations nor part of higher‑rank Teichmüller theory. The authors build cyclic G₂′–Higgs bundles, called α‑bundles and β‑bundles, inside special slices of the Lie algebra linked to the two simple roots of 𝔤₂^ℂ. Using the non‑abelian Hodge correspondence, each such bundle yields a representation π₁(S)→G₂′. They prove that every polystable α‑bundle gives a P_α‑Anosov representation, while most β‑bundles that are also Hodge bundles are P_β‑Anosov. The paper also shows that the fundamental group of a certain locally homogeneous G₂′/P_σ–manifold is an invariant of the connected component of the representation. This leads to lower bounds on how many distinct connected components of P_α‑ and P_β‑Anosov representations exist inside the two non‑Hitchin parts of the G₂′ character variety: at least 3g–4 and 3g–3 components in one part, and at least 2g–2 in the other. The authors note that their proof for P_β‑Anosov representations applies only to Hodge β‑bundles; it does not yet cover all β‑bundles. These results broaden the known landscape of exotic representation components in higher‑rank groups and highlight new geometric structures arising from Higgs bundle techniques.

Source paper

$G_2'$-Slodowy Slices II: Anosov Representations

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New Exotic Pieces of the Character Variety of Surface Groups in the Group G₂′ | arXiv News