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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Momentum Maps for Smooth Projective Unitary Representations
verfasst von : Bas Janssens, Karl-Hermann Neeb
Erschienen in: Geometric Methods in Physics
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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.