Character Theory for Semilinear Representations

Fuente: arXiv
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Main Author: Taylor, James
Format: Preprint
Published: 2025
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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