Un caractère relatif pondéré
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914209300742144 |
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| author | Chaudouard, Pierre-Henri |
| author_facet | Chaudouard, Pierre-Henri |
| contents | Let $p\geq 1$. The symmetric space $S=GL(2p+1)/GL(p+1)\times GL(p)$ (over a number field) is not cuspidal in the sense that its automorphic spectrum does not contain any cuspidal representation of $GL(2p+1)$. In this article, we compute the spectral decomposition of its relatively cuspidal part: this is, by definition, the part of the spectrum that is induced from the cuspidal part of the symmetric space $(GL(1)\times GL(2p)) / (GL(1)\times GL(p)\times GL(p))$. As an application, we obtain the expression of the contribution of this relatively cuspidal part to the Guo-Jacquet trace formula (established by H. Li and the author) in terms of a weighted relative character. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_17056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Un caractère relatif pondéré Chaudouard, Pierre-Henri Representation Theory Number Theory 11F70 Let $p\geq 1$. The symmetric space $S=GL(2p+1)/GL(p+1)\times GL(p)$ (over a number field) is not cuspidal in the sense that its automorphic spectrum does not contain any cuspidal representation of $GL(2p+1)$. In this article, we compute the spectral decomposition of its relatively cuspidal part: this is, by definition, the part of the spectrum that is induced from the cuspidal part of the symmetric space $(GL(1)\times GL(2p)) / (GL(1)\times GL(p)\times GL(p))$. As an application, we obtain the expression of the contribution of this relatively cuspidal part to the Guo-Jacquet trace formula (established by H. Li and the author) in terms of a weighted relative character. |
| title | Un caractère relatif pondéré |
| topic | Representation Theory Number Theory 11F70 |
| url | https://arxiv.org/abs/2512.17056 |