On the dual of complex Olshanskii semigroups
| dc.creator | Kroetz, Bernhard | |
| dc.date | 2000-06-26 | |
| dc.date.accessioned | 2026-07-07T04:36:06Z | |
| dc.date.available | 2026-07-07T04:36:06Z | |
| dc.description | Let $G$ be a connected Lie group and $\hat G$ its unitary dual. We are interested in the part $Λ\subset\hat G$ which corresponds to the unitary highest weight representations of $G$. Then there are several topologies on $Λ$: The euclidean topology $T_E$ which comes from the identification of $Λ$ with the set of highest weights, the induced topology $T_I$ induced from the Fell topology on $\hat G$ and finally a natural topology $T_S$ which comes from the hull kernel topology of certain CCR C^*-algebras which are related to the holomorphic extemsion of unitary highest weight representations to complex Olshanskii semigroups $S$. One of the main results in this paper is the inclusion chain $T_S\subset T_I\subset T_E$. Further we exhibit very large interesting subspaces of $Λ$ where these topologies coincide. Finally we show that the Borel structures on $Λ$ induced from the three different topologies coincide. | |
| dc.description | 19 pages, to appear in Mathematische Zeitschrift | |
| dc.identifier | https://arxiv.org/abs/math/0006200 | |
| dc.identifier | http://arxiv.org/abs/math/0006200 | |
| dc.identifier | Math. Z. 237(3) (2001), 505-529 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59483 | |
| dc.subject | Representation Theory | |
| dc.subject | Operator Algebras | |
| dc.title | On the dual of complex Olshanskii semigroups | |
| dc.type | text |