TY - JOUR
T1 - Projective unitary representations of infinite dimensional Lie groups
AU - Janssens, B.
AU - Neeb, Karl-Hermann
PY - 2019
Y1 - 2019
N2 - 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♯.
AB - 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♯.
UR - http://www.scopus.com/inward/record.url?scp=85069734869&partnerID=8YFLogxK
U2 - 10.1215/21562261-2018-0016
DO - 10.1215/21562261-2018-0016
M3 - Article
SN - 0023-608X
VL - 59
SP - 293
EP - 341
JO - Kyoto Journal of Mathematics
JF - Kyoto Journal of Mathematics
IS - 2
ER -