On the relative Langlands duality for $\operatorname{Sp}_{2n} \backslash \operatorname{GL}_{2n+1}$ (with an appendix by Zeyu Wang)
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908338195791872 |
|---|---|
| author | Lu, Weixiao Wang, Zeyu Xi, Guodong |
| author_facet | Lu, Weixiao Wang, Zeyu Xi, Guodong |
| contents | We verify the relative Langlands duality conjecture proposed by Ben-Zvi, Sakellaridis, Venkatesh for the hyperspherical Hamiltonian variety $T^*(\operatorname{Sp}_{2n}\backslash \operatorname{GL}_{2n+1})$. We provide numerical (over number fields and function fields) and geometric (in the étale setting) evidence that its dual Hamiltonian variety should be $T^*(\operatorname{GL}_n \times \operatorname{GL}_{n+1} \backslash \operatorname{GL}_{2n+1})$ as is predicted by Ben-Zvi, Sakellaridis, Venkatesh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the relative Langlands duality for $\operatorname{Sp}_{2n} \backslash \operatorname{GL}_{2n+1}$ (with an appendix by Zeyu Wang) Lu, Weixiao Wang, Zeyu Xi, Guodong Representation Theory Number Theory We verify the relative Langlands duality conjecture proposed by Ben-Zvi, Sakellaridis, Venkatesh for the hyperspherical Hamiltonian variety $T^*(\operatorname{Sp}_{2n}\backslash \operatorname{GL}_{2n+1})$. We provide numerical (over number fields and function fields) and geometric (in the étale setting) evidence that its dual Hamiltonian variety should be $T^*(\operatorname{GL}_n \times \operatorname{GL}_{n+1} \backslash \operatorname{GL}_{2n+1})$ as is predicted by Ben-Zvi, Sakellaridis, Venkatesh. |
| title | On the relative Langlands duality for $\operatorname{Sp}_{2n} \backslash \operatorname{GL}_{2n+1}$ (with an appendix by Zeyu Wang) |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2504.18774 |