Projective unitary representations of infinite-dimensional Lie groups

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Janssens B, Neeb KH
Zeitschrift: Kyoto Journal of Mathematics
Jahr der Veröffentlichung: 2019
Band: 59
Heftnummer: 2
Seitenbereich: 293-341
ISSN: 2156-2261
eISSN: 2154-3321 ​


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(#).


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Neeb, Karl-Hermann Prof. Dr.
Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)


Einrichtungen weiterer Autorinnen und Autoren

Delft University of Technology


Zitierweisen

APA:
Janssens, B., & Neeb, K.-H. (2019). Projective unitary representations of infinite-dimensional Lie groups. Kyoto Journal of Mathematics, 59(2), 293-341. https://dx.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.

BibTeX: 

Zuletzt aktualisiert 2019-21-06 um 09:03