On Unstable Principal Bundles over Elliptic Curves

This article is an outgrowth of a more comprehensive project to provide a detailed account for the results announced in [13], [14]. In these reports a relation between simple elliptic singularities in the sense of Saito [22] and certain holomorphic Kac-Moody loop groups LG is established which generalizes a well known theorem of Brieskorn [6], cf. also [26], relating simple singularities of type A , D , E and the corresponding simple algebraic groups G. An important ingredient in the derivation of Brieskorn’s result is the orbital geometry of the unipotent variety U(G) of G, especially in the neighborhood of a subregular unipotent orbit. In our generalization, the unipotent variety U(G) is replaced by an ‘unstable’ variety U(LG) in LG whose orbital geometry can be described, essentially