Projective unitary representations of infinite dimensional Lie groups

B. Janssens, Karl-Hermann Neeb

Research output: Contribution to journalArticleScientificpeer-review


For an infinite dimensional Lie group G modelled 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 modelled on a barrelled 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♯.
Original languageEnglish
Pages (from-to)293-341
Number of pages49
JournalKyoto Journal of Mathematics
Issue number2
Publication statusPublished - 2019


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