Character Theory for Semilinear Representations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914478145142784 |
|---|---|
| author | Taylor, James |
| author_facet | Taylor, James |
| contents | Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the category of semilinear representations of $G$ over $L$ can be described in terms of the category of linear representations of $H$, the kernel of the map $G \rightarrow \mathrm{Aut}(L)$. When $G$ is finite and $L$ has characteristic 0 this provides a character theory for semilinear representations of $G$ over $L$, which recovers ordinary character theory when the action of $G$ on $L$ is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Character Theory for Semilinear Representations Taylor, James Representation Theory Group Theory Number Theory Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the category of semilinear representations of $G$ over $L$ can be described in terms of the category of linear representations of $H$, the kernel of the map $G \rightarrow \mathrm{Aut}(L)$. When $G$ is finite and $L$ has characteristic 0 this provides a character theory for semilinear representations of $G$ over $L$, which recovers ordinary character theory when the action of $G$ on $L$ is trivial. |
| title | Character Theory for Semilinear Representations |
| topic | Representation Theory Group Theory Number Theory |
| url | https://arxiv.org/abs/2511.04296 |