On Arthur representations and the unitary dual
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914316366643200 |
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| author | Hazeltine, Alexander Jiang, Dihua Liu, Baiying Lo, Chi-Heng Zhang, Qing |
| author_facet | Hazeltine, Alexander Jiang, Dihua Liu, Baiying Lo, Chi-Heng Zhang, Qing |
| contents | In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This conjecture provides a candidate set for the unitary dual, constructed from Arthur representations. For classical groups, we develop an explicit algorithm to generate this candidate set. Evidence for its exhaustiveness includes compatibility with the known generic unitary dual, unramified unitary dual, and low-corank representations. As further support, we verify the conjecture for the unitary dual of the exceptional group of type $G_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Arthur representations and the unitary dual Hazeltine, Alexander Jiang, Dihua Liu, Baiying Lo, Chi-Heng Zhang, Qing Representation Theory Number Theory In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This conjecture provides a candidate set for the unitary dual, constructed from Arthur representations. For classical groups, we develop an explicit algorithm to generate this candidate set. Evidence for its exhaustiveness includes compatibility with the known generic unitary dual, unramified unitary dual, and low-corank representations. As further support, we verify the conjecture for the unitary dual of the exceptional group of type $G_2$. |
| title | On Arthur representations and the unitary dual |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2410.11806 |