Archimedean Distinguished Representations and Exceptional Poles
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913610866884608 |
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| author | Yadav, Akash |
| author_facet | Yadav, Akash |
| contents | Let $F$ be an archimedean local field and let $E$ be $F\times F$ (resp. a quadratic extension of $F$). We prove that an irreducible generic (resp. nearly tempered) representation of $\operatorname{GL}_n(E)$ is $\operatorname{GL}_n(F)$ distinguished if and only if its Rankin-Selberg (resp. Asai) $L$-function has an exceptional pole of level zero at $0$. Further, we deduce a necessary condition for the ramification of such representations using the theory of weak test vectors developed by Humphries and Jo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Archimedean Distinguished Representations and Exceptional Poles Yadav, Akash Number Theory Representation Theory 11F70, 22E55 Let $F$ be an archimedean local field and let $E$ be $F\times F$ (resp. a quadratic extension of $F$). We prove that an irreducible generic (resp. nearly tempered) representation of $\operatorname{GL}_n(E)$ is $\operatorname{GL}_n(F)$ distinguished if and only if its Rankin-Selberg (resp. Asai) $L$-function has an exceptional pole of level zero at $0$. Further, we deduce a necessary condition for the ramification of such representations using the theory of weak test vectors developed by Humphries and Jo. |
| title | Archimedean Distinguished Representations and Exceptional Poles |
| topic | Number Theory Representation Theory 11F70, 22E55 |
| url | https://arxiv.org/abs/2401.09063 |