1. Triality and automorphisms of principal bundles moduli spaces.
- Author
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Antón-Sancho, Álvaro
- Subjects
- *
AUTOMORPHISMS , *RIEMANN surfaces - Abstract
Let X be a compact Riemann surface of genus g ≥ 2 and let G be the group Spin(8, ℂ) or PSO(8, ℂ). Let τ be a choice of a non-trivial outer automorphism of G of order 3, called triality. Suppose that X is equipped with a holomorphic order 3 automorphism α. Then α acts on the moduli space M(G) of principal G-bundles over X by taking the pull-back, and τ also acts on M(G), by modifying the action of G on the principal bundles through any automorphism of G of order 3 representing τ. The combination of these two actions gives an automorphism of order 3 of the moduli space M(G). In this work, the notion of α-trialitarian G-bundle is introduced to describe the fixed points of the automorphism of M(G) mentioned above. In particular, an equivalent notion of stability and polystability for such bundles is proved, and an explicit construction of them is provided. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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