Karl-Hermann Neeb (Erlangen-Nürnberg):

Positive energy representations of gauge groups

We report on a joint project with Bas Janssens on unitary representations of gauge groups Gauc(P) (compactly supported gauge transformations) of a principal bundle P with compact structure group K over a smooth manifold. We consider representations which are covariant with respect to a smooth R-action by automorphisms on the bundle P for which the corresponding flow on M has no fixed points. If M is compact and the flow on M is periodic, then all irreducible representations of this type are finite tensor products of representations of twisted loop groups obtained by restrictions to finitely many orbits in M. If M is not compact, then locally finite sets of orbits in M lead to infinite tensor products which can be controlled by suitable C*-algebras.
close window