Momentum maps for smooth projective unitary representations
Janssens B, Neeb KH (2016)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2016
Publisher: Springer-Birkhäuser
Edited Volumes: Geometric Methods in Physics. XXXIV Workshop 2015
Series: Trends in Mathematics
Book Volume: II
Pages Range: 115-127
ISBN: 978-3-319-31755-7
URI: https://arxiv.org/abs/1510.08257
DOI: 10.1007/978-3-319-31756-4_12
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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APA:
Janssens, B., & Neeb, K.H. (2016). Momentum maps for smooth projective unitary representations. In Kielanowski P., Bieliavsky P., Odesskii A., Odzijewicz A., Schlichenmaier M., Voronov T. (Eds.), Geometric Methods in Physics. XXXIV Workshop 2015. (pp. 115-127). Springer-Birkhäuser.
MLA:
Janssens, Bas, and Karl Hermann Neeb. "Momentum maps for smooth projective unitary representations." Geometric Methods in Physics. XXXIV Workshop 2015. Ed. Kielanowski P., Bieliavsky P., Odesskii A., Odzijewicz A., Schlichenmaier M., Voronov T., Springer-Birkhäuser, 2016. 115-127.
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