Galois E6-Bundles over a Hyperelliptic Algebraic Curve.

Let X be a hyperelliptic algebraic curve and let M (E 6) be the moduli space of polystable principal E 6 -bundles over X. Suppose, in addition, that the outer involution σ of E 6 acts as the hyperelliptic involution of X. Then, an automorphism of M (E 6) is defined which acts by E ↦ σ ∗ (E ∗) , where E is a principal E 6 -bundle over X seen as a vector bundle through the fundamental irreducible 27-dimensional representation of E 6 . In this paper, Galois E 6 -bundles over X are defined and related to the fixed points of the above automorphism of M (E 6) . If P E 6 is the centerless group with Lie algebra e 6 , then Galois P E 6 -bundles over X are also defined and related to Galois E 6 -bundles. Finally, a specific expression for a certain family of Galois E 6 -bundles over X is given and some implications of the study in terms of representations of the fundamental group π 1 (X) of the base curve are drawn. [ABSTRACT FROM AUTHOR]