Projective unitary representations of infinite-dimensional Lie groups

Janssens B, Neeb KH (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Kyoto Journal of Mathematics Duke University Press

Book Volume: 59

Pages Range: 293-341

Journal Issue: 2

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(#).

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Delft University of Technology (TU Delft) NL Netherlands (NL)

How to cite

APA:

Janssens, B., & Neeb, K.H. (2019). Projective unitary representations of infinite-dimensional Lie groups. Kyoto Journal of Mathematics, 59(2), 293-341. https://doi.org/10.1215/21562261-2018-0016

MLA:

Janssens, Bas, and Karl Hermann Neeb. "Projective unitary representations of infinite-dimensional Lie groups." Kyoto Journal of Mathematics 59.2 (2019): 293-341.

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