2024
DOI: 10.1515/crelle-2024-0083
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Covariant projective representations of Hilbert–Lie groups

Karl-Hermann Neeb,
Francesco G. Russo

Abstract: Hilbert–Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. In this paper, we study unitary representations of these groups from various perspectives. First, we address norm-continuous, also called bounded, representations. These are well known for simple groups, but the general picture is more complicated. Our first main result is a characterization… Show more

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