PreprintCC BY 4.0arXiv
The fields generated by character values of linear and unitary groups
Abstract
For a finite group G, define the field ℚ(G) := ℚ({χ(g) : χ∈ Irr(G) , g ∈ G}). In this article we compute generating sets for the fields ℚ(G) when G is a finite general or special linear group, a finite general or special unitary group, or one of the simple groups PSLn(q) or PSUn(q). We then apply these results to classify all number fields F of degree $2$ or $3$ over ℚ such that F = ℚ(S) for some non-abelian simple group S.
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BibTeX
@misc{ketchum2026fields,
title = {{The fields generated by character values of linear and unitary groups}},
author = {Eden Ketchum},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35183},
eprint = {2609.35183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35183},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The fields generated by character values of linear and unitary groups
AU - Eden Ketchum
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35183
UR - https://arxiv.org/abs/2609.35183
AB - For a finite group G, define the field ℚ(G) := ℚ({χ(g) : χ∈ Irr(G) , g ∈ G}). In this article we compute generating sets for the fields ℚ(G) when G is a finite general or special linear group, a finite general or special unitary group, or one of the simple groups PSL_n(q) or PSU_n(q). We then apply these results to classify all number fields F of degree $2$ or $3$ over ℚ such that F = ℚ(S) for some non-abelian simple group S.
ER -