Neeb, Karl-Hermann (2000)
Representation theory and convexity.
In: Transformation groups, 5 (4)
doi: 10.1007/BF01234796
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
IfS=G Exp (iW) is a complex open Ol'shanskiî semigroup, whereW is an open elliptic cone, then we considerG-biinvariant domainsD=G Exp (iD g)S. First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG. In the second part of the paper we explain how to construct biinvariant Kähler structures on biinvariant Stein domains and show by a certain Legendre transform that the so obtained symplectic manifolds are isomorphic to domains in the cotangent bundleT * (G).
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2000 |
| Autor(en): | Neeb, Karl-Hermann |
| Art des Eintrags: | Bibliographie |
| Titel: | Representation theory and convexity |
| Sprache: | Englisch |
| Publikationsjahr: | 1 Dezember 2000 |
| Verlag: | Birkhäuser |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Transformation groups |
| Jahrgang/Volume einer Zeitschrift: | 5 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.1007/BF01234796 |
| Kurzbeschreibung (Abstract): | IfS=G Exp (iW) is a complex open Ol'shanskiî semigroup, whereW is an open elliptic cone, then we considerG-biinvariant domainsD=G Exp (iD g)S. First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG. In the second part of the paper we explain how to construct biinvariant Kähler structures on biinvariant Stein domains and show by a certain Legendre transform that the so obtained symplectic manifolds are isomorphic to domains in the cotangent bundleT * (G). |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik |
| Hinterlegungsdatum: | 20 Nov 2008 08:18 |
| Letzte Änderung: | 27 Jul 2023 11:23 |
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