Weak unipotence and Langlands duality
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_ | 1866917016527437824 |
|---|---|
| author | Ma, Jia-jun Yu, Shilin |
| author_facet | Ma, Jia-jun Yu, Shilin |
| contents | Weak unipotence of primitive ideals is a crucial property in the study of unitary representations of reductive groups. We establish a sufficient condition, referred to as mild unipotence, which guarantees weak unipotence and is more accessible in practice. We establish mild unipotence for both the $q$-unipotent ideals defined by McGovern and unipotent ideals attached to nilpotent orbit covers defined by Losev-Mason-Brown-Matvieievskyi (arXiv:2108.03453 [math.RT]). Our proof is conceptual and uses the bijection between special orbits in type $D$ and metaplectic special orbits in type $C$ found by Barbasch-Ma-Sun-Zhu (arXiv:2010.16089 [math.RT]) in an essential way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak unipotence and Langlands duality Ma, Jia-jun Yu, Shilin Representation Theory 22E46, 16D60 Weak unipotence of primitive ideals is a crucial property in the study of unitary representations of reductive groups. We establish a sufficient condition, referred to as mild unipotence, which guarantees weak unipotence and is more accessible in practice. We establish mild unipotence for both the $q$-unipotent ideals defined by McGovern and unipotent ideals attached to nilpotent orbit covers defined by Losev-Mason-Brown-Matvieievskyi (arXiv:2108.03453 [math.RT]). Our proof is conceptual and uses the bijection between special orbits in type $D$ and metaplectic special orbits in type $C$ found by Barbasch-Ma-Sun-Zhu (arXiv:2010.16089 [math.RT]) in an essential way. |
| title | Weak unipotence and Langlands duality |
| topic | Representation Theory 22E46, 16D60 |
| url | https://arxiv.org/abs/2510.13523 |