Another proof for the continuity of the Lipsman mapping
UDC 515.1 We consider the semidirect product $G = K \ltimes V$ where $K$ is a connected compact Lie group acting by automorphisms on a finite dimensional real vector space $V$ equipped with an inner product $\langle , \rangle$. By $\hat G $ we denote the unitary dual of $G$ and by ${\mathfrak{g}^{ \...
Saved in:
| Date: | 2020 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/548 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 515.1
We consider the semidirect product $G = K \ltimes V$ where $K$ is a connected compact Lie group acting by automorphisms on a finite dimensional real vector space $V$ equipped with an inner product $\langle , \rangle$. By $\hat G $ we denote the unitary dual of $G$ and by ${\mathfrak{g}^{ \ddagger} /} G$ the space of admissible coadjoint orbits, where $\mathfrak{g}$ is the Lie algebra of $G$. It was pointed out by Lipsman that the correspondence between $\hat{G} $ and ${\mathfrak{g}^{ \ddagger} /} G$ is bijective. Under some assumption on $G$, we give another proof for the continuity of the orbit mapping (Lipsman mapping)$$\Theta : {\mathfrak{g}^{ \ddagger} /} G - \rightarrow \hat{G} .$$ |
|---|---|
| DOI: | 10.37863/umzh.v72i7.548 |