Loop groups, elliptic singularities and principal bundles over elliptic curves
Volume 62 / 2003
Banach Center Publications 62 (2003), 87-99
MSC: Primary: 14B07, 14L32. Secondary: 14H52, 14H60, 32S25
DOI: 10.4064/bc62-0-6
Abstract
There is a well known relation between simple algebraic groups and simple singularities, cf. \cite{Br70}, \cite{Sl80}. The simple singularities appear as the generic singularity in codimension two of the unipotent variety of simple algebraic groups. Furthermore, the semi-universal deformation and the simultaneous resolution of the singularity can be constructed in terms of the algebraic group. The aim of these notes is to extend this kind of relation to loop groups and simple elliptic singularities. It is the successful completion of work begun long ago, \cite{Sl81}, cf. also \cite{Sl85A}, \cite{Sl84}, \cite{Sl85B} for more general situations.
