Clebsch-Gordan and the theta filtration for modular representations of $\mathrm{GL}_2({\mathbb F}_q)$
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_ | 1866915595409162240 |
|---|---|
| author | Bhattacharjee, Srijeet Ghate, Eknath Pandey, Shivansh Veerapaneni, Sriram |
| author_facet | Bhattacharjee, Srijeet Ghate, Eknath Pandey, Shivansh Veerapaneni, Sriram |
| contents | Let $p$ be a prime. We solve two problems in the mod $p$ representation theory of $\mathrm{GL}_2(\mathbb{F}_{q})$ where $q=p^f$. We first prove a Clebsch-Gordan decomposition theorem for the tensor product of two mod $p$ representations of $\mathrm{GL}_2(\mathbb{F}_{q})$. As an application, we use this to guess the structure of quotients of symmetric power representations of $\mathrm{GL}_2(\mathbb{F}_{q})$ by submodules in the theta filtration. We then give a direct proof of this structure showing that such quotients are built out of principal series representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clebsch-Gordan and the theta filtration for modular representations of $\mathrm{GL}_2({\mathbb F}_q)$ Bhattacharjee, Srijeet Ghate, Eknath Pandey, Shivansh Veerapaneni, Sriram Representation Theory Number Theory Let $p$ be a prime. We solve two problems in the mod $p$ representation theory of $\mathrm{GL}_2(\mathbb{F}_{q})$ where $q=p^f$. We first prove a Clebsch-Gordan decomposition theorem for the tensor product of two mod $p$ representations of $\mathrm{GL}_2(\mathbb{F}_{q})$. As an application, we use this to guess the structure of quotients of symmetric power representations of $\mathrm{GL}_2(\mathbb{F}_{q})$ by submodules in the theta filtration. We then give a direct proof of this structure showing that such quotients are built out of principal series representations. |
| title | Clebsch-Gordan and the theta filtration for modular representations of $\mathrm{GL}_2({\mathbb F}_q)$ |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2511.02299 |