Journal article
Analytic continuation of local representations of symmetric spaces
Journal of functional analysis, Vol.70(2), pp.304-322
1987
DOI: 10.1016/0022-1236(87)90115-7
Abstract
We prove the following analytic continuation theorem which applies to any virtual representation of any symmetric space ( G , K , σ ). The problem of passing from the Euclidean group to the Poincaré group appears first to have been addressed and solved this way by Klein and Landau. Let G be a Lie group, K a closed subgroup, and σ an involutive automorphism with K as fixed-point subgroup. If g = k + m is the corresponding symmetric Lie algebra, we form g ∗ = k + im , and let G ∗ denote the simply connected Lie group with g ∗ as Lie algebra. We consider virtual representations π of G on a fixed complex Hilbert space H , adopting the definitions due to J. Fröhlich, K. Osterwalder, and E. Seiler; in particular, π(g −1 ) ⊂ π(σ(g)) ∗ (possibly unbounded operators) for g in a neighborhood of e in G. We prove that every such π continues analytically to a strongly continuous unitary representation of G ∗ on H . Our theorem extends results due to Klein-Landau, Fröhlich et al. , and others, earlier, for special cases. Previous results were known only for special ( G , K , σ ), and then only for certain π.
Details
- Title: Subtitle
- Analytic continuation of local representations of symmetric spaces
- Creators
- Palle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.70(2), pp.304-322
- DOI
- 10.1016/0022-1236(87)90115-7
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1987
- Academic Unit
- Mathematics
- Record Identifier
- 9983985988802771
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