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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1710.10190 |
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| _version_ | 1866909982779244544 |
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| author | Harris, Benjamin Oshima, Yoshiki |
| author_facet | Harris, Benjamin Oshima, Yoshiki |
| contents | When $G_{\mathbb{R}}$ is a real, linear algebraic group, the orbit method predicts that nearly all of the unitary dual of $G_{\mathbb{R}}$ consists of representations naturally associated to orbital parameters $(\mathcal{O},Γ)$. If $G_{\mathbb{R}}$ is a real, reductive group and $\mathcal{O}$ is a semisimple coadjoint orbit, the corresponding unitary representation $π(\mathcal{O},Γ)$ may be constructed utilizing Vogan and Zuckerman's cohomological induction together with Mackey's real parabolic induction. In this article, we give a geometric character formula for such representations $π(\mathcal{O},Γ)$. Special cases of this formula were previously obtained by Harish-Chandra and Kirillov when $G_{\mathbb{R}}$ is compact and by Rossmann and Duflo when $π(\mathcal{O},Γ)$ is tempered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_10190 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Irreducible Characters and Semisimple Coadjoint Orbits Harris, Benjamin Oshima, Yoshiki Representation Theory When $G_{\mathbb{R}}$ is a real, linear algebraic group, the orbit method predicts that nearly all of the unitary dual of $G_{\mathbb{R}}$ consists of representations naturally associated to orbital parameters $(\mathcal{O},Γ)$. If $G_{\mathbb{R}}$ is a real, reductive group and $\mathcal{O}$ is a semisimple coadjoint orbit, the corresponding unitary representation $π(\mathcal{O},Γ)$ may be constructed utilizing Vogan and Zuckerman's cohomological induction together with Mackey's real parabolic induction. In this article, we give a geometric character formula for such representations $π(\mathcal{O},Γ)$. Special cases of this formula were previously obtained by Harish-Chandra and Kirillov when $G_{\mathbb{R}}$ is compact and by Rossmann and Duflo when $π(\mathcal{O},Γ)$ is tempered. |
| title | Irreducible Characters and Semisimple Coadjoint Orbits |
| topic | Representation Theory |
| url | https://arxiv.org/abs/1710.10190 |