Momentum Maps for Smooth Projective Unitary Representations

Abstract

For a smooth projective unitary representation (ρ,H) of a locally convex Lie group G, the projective space P(H∞) of smooth vectors is a locally convex Kähler manifold. We show that the action of G on P(H∞) is weakly Hamiltonian, and lifts to a Hamiltonian action of the central U(1)- extension G^# obtained from the projective representation. We identify the non-equivariance cocycles obtained from the weakly Hamiltonian action with those obtained from the projective representation, and give some integrality conditions on the image of the momentum map.

Mathematics Subject Classification (2010). 20C25, 37J15.