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@article{faucris.262982705,
abstract = {Let (G, tau) be a finite-dimensional Lie group with an involutive automorphism tau of G and let g = h circle plus q be its corresponding Lie algebra decomposition. We show that every nondegenerate strongly continuous representation on a complex Hilbert space 7-t of an open *-subsemigroup S subset of G, where s* = tau(s) -1, has an analytic extension to a strongly continuous unitary representation of the 1-connected Lie group G(1)(c) with Lie algebra [q, q] circle plus iq. We further examine the minimal conditions under which an analytic extension to the 1-connected Lie group G(c) with Lie algebra h circle plus iq exists. This result generalizes the Lascher-Mack theorem and the extensions of the Lascher-Mack theorem for *subsemigroups satisfying S = S(G(tau))(0) by Merigon, Neeb, and Olafsson. Finally, we prove that nondegenerate strongly continuous representations of certain *-subsemigroups S can even be extended to representations of a generalized version of an Olshanski semigroup.},
author = {Oeh, Daniel},
doi = {10.1093/imrn/rnz342},
faupublication = {yes},
journal = {International Mathematics Research Notices},
note = {CRIS-Team WoS Importer:2021-08-20},
pages = {6200-6245},
peerreviewed = {Yes},
title = {{Analytic} {Extensions} of {Representations} of *-{Subsemigroups} {Without} {Polar} {Decomposition}},
volume = {2021},
year = {2021}
}