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

Let X be a compact algebraic curve of genus g ≥ 2. The nontrivial outer automorphism σ of the complex Lie group E6 acts on the moduli space M(E6) of principal E6-bundles over X , and this action defines an automorphism fσ of M(E6). The group H1(X, Z (E6)) of principal Z(E6)-bundles over X also acts on M(E6) by tensor product, Z(E6) being the center of E6, so each choice of an element L ∈ H1(X, Z(E6)) defines an automorphism fL of M(E6). In this paper two theorems describing the simple fixed points of the automorphism fL of M(E6) and the composition fL◦fσ are proved.