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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.09826 |
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| _version_ | 1866910471446069248 |
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| author | Beltita, Ingrid van Velthoven, Jordy Timo |
| author_facet | Beltita, Ingrid van Velthoven, Jordy Timo |
| contents | For an exponential Lie group $G$ and an irreducible unitary representation $(π,\mathcal{H}_π)$ of $G$, we consider the natural action defined by $π$ on the projective space of $\mathcal{H}_π$, and show that the stabilisers of this action coincide with the projective kernel of $π$. Using this, we prove that, if $G/\mathrm{pker}(π)$ is unimodular, then $π$ admits a symplectic projective orbit if and only if $π$ is square-integrable modulo its projective kernel $\mathrm{pker}(π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symplectic projective orbits of unimodular exponential Lie groups Beltita, Ingrid van Velthoven, Jordy Timo Representation Theory For an exponential Lie group $G$ and an irreducible unitary representation $(π,\mathcal{H}_π)$ of $G$, we consider the natural action defined by $π$ on the projective space of $\mathcal{H}_π$, and show that the stabilisers of this action coincide with the projective kernel of $π$. Using this, we prove that, if $G/\mathrm{pker}(π)$ is unimodular, then $π$ admits a symplectic projective orbit if and only if $π$ is square-integrable modulo its projective kernel $\mathrm{pker}(π)$. |
| title | Symplectic projective orbits of unimodular exponential Lie groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2402.09826 |