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.