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arXiv · 1510.08257

Momentum Maps for Smooth Projective Unitary Representations

Bas Janssens·Karl-Hermann Neeb
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Abstract

For a smooth projective unitary representation of a locally convex Lie group G, the projective space of smooth vectors is a locally convex Kaehler manifold. We show that the action of G on this space is weakly Hamiltonian, and lifts to a Hamiltonian action of the central U(1)-extension of 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.

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BibTeXRIS

Bas Janssens, Karl-Hermann Neeb. 2015-10-28. Momentum Maps for Smooth Projective Unitary Representations. https://arxiv.org/abs/1510.08257

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