AG Lie-Gruppen: B. Janssens, TU Delft: Positive energy representations of compactly supported diffeomorphism groups

Positive energy representations of compactly supported diffeomorphism groups –
Vortragender: Bas Janssens, Delft University of Technology – Einladender:
Karl-Hermann Neeb

Abstract: Let M be a manifold, and let \\phi_t be a distinguished 1-parameter
flow of time translations. A projective unitary representation \\rho of
Diff_c(M) is of positive energy with respect to \\phi_t if it extends to the
semidirect product of Diff_c(M) with the group (R,+) of time translations in
such a way that the generator of the time translations (the Hamiltonian) has
spectrum bounded from below. We show that for dim(M)>1, every positive energy
representation of Diff_c(M) is trivial.

(Joint work with Milan Niestijl)