The local converse theorem for quasi-split $O_{2n}$ and $SO_{2n}$
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908707658399744 |
|---|---|
| author | Haan, Jaeho Kim, Yeansu Kwon, Sanghoon |
| author_facet | Haan, Jaeho Kim, Yeansu Kwon, Sanghoon |
| contents | Let $F$ be a non-archimedean local field of characteristic not equal to 2. In this paper, we prove the local converse theorem for quasi-split $Ø_{2n}(F)$ and $\SO_{2n}(F)$, via the description of the local theta correspondence between $Ø_{2n}(F)$ and $\Sp_{2n}(F)$. More precisely, as a main step, we explicitly describe the precise behavior of the $γ$-factors under the correspondence. Furthermore, we apply our results to prove the weak rigidity theorems for irreducible generic cuspidal automorphic representations of $Ø_{2n}(\A)$ and $\SO_{2n}(\mathbb{A})$, respectively, where $\A$ is a ring of adele of a global number field $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12693 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The local converse theorem for quasi-split $O_{2n}$ and $SO_{2n}$ Haan, Jaeho Kim, Yeansu Kwon, Sanghoon Number Theory Representation Theory Let $F$ be a non-archimedean local field of characteristic not equal to 2. In this paper, we prove the local converse theorem for quasi-split $Ø_{2n}(F)$ and $\SO_{2n}(F)$, via the description of the local theta correspondence between $Ø_{2n}(F)$ and $\Sp_{2n}(F)$. More precisely, as a main step, we explicitly describe the precise behavior of the $γ$-factors under the correspondence. Furthermore, we apply our results to prove the weak rigidity theorems for irreducible generic cuspidal automorphic representations of $Ø_{2n}(\A)$ and $\SO_{2n}(\mathbb{A})$, respectively, where $\A$ is a ring of adele of a global number field $L$. |
| title | The local converse theorem for quasi-split $O_{2n}$ and $SO_{2n}$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2301.12693 |