Fixed points of principal E ₆-bundles over a compact algebraic curve

Abstract

Let X be a compact algebraic curve of genus g ≥ 2. The nontrivial outer automorphism σ of the complex Lie group E ₆ acts on the moduli space M(E ₆) of principal E ₆-bundles over X , and this action defines an automorphism f_σ of M(E ₆). The group H ¹(X, Z (E ₆)) of principal Z(E ₆)-bundles over X also acts on M(E ₆) by tensor product, Z(E ₆) being the center of E ₆, so each choice of an element L ∈ H ¹(X, Z(E ₆)) defines an automorphism f_L of M(E ₆). In this paper two theorems describing the simple fixed points of the automorphism f_L of M(E ₆) and the composition f_L ◦f_σ are proved.