arXiv
Open Access
2025
Character Theory for Semilinear Representations
James Taylor
Abstrak
Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the irreducible semilinear representations of $G$ over $L$ can be completely described in terms of irreducible linear representations of $H$, the kernel of the map $G \rightarrow \mathrm{Aut}(L)$. When $G$ is finite and $|G| \in L^{\times}$ 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.
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James Taylor
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2025
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓