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June 2019 Projective unitary representations of infinite-dimensional Lie groups
Bas Janssens, Karl-Hermann Neeb
Kyoto J. Math. 59(2): 293-341 (June 2019). DOI: 10.1215/21562261-2018-0016

Abstract

For an infinite-dimensional Lie group G modeled on a locally convex Lie algebra g, we prove that every smooth projective unitary representation of G corresponds to a smooth linear unitary representation of a Lie group extension G of G. (The main point is the smooth structure on G.) For infinite-dimensional Lie groups G which are 1-connected, regular, and modeled on a barreled Lie algebra g, we characterize the unitary g-representations which integrate to G. Combining these results, we give a precise formulation of the correspondence between smooth projective unitary representations of G, smooth linear unitary representations of G, and the appropriate unitary representations of its Lie algebra g.

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Bas Janssens. Karl-Hermann Neeb. "Projective unitary representations of infinite-dimensional Lie groups." Kyoto J. Math. 59 (2) 293 - 341, June 2019. https://doi.org/10.1215/21562261-2018-0016

Information

Received: 17 February 2016; Revised: 17 January 2017; Accepted: 15 February 2017; Published: June 2019
First available in Project Euclid: 2 April 2019

zbMATH: 07080106
MathSciNet: MR3960295
Digital Object Identifier: 10.1215/21562261-2018-0016

Subjects:
Primary: 17B15

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 2 • June 2019
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