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Explicit invariants of the Suzuki and Ree groups in their function fields
Abstract
The Suzuki and Ree curves are two classical Deligne--Lusztig curves. They are maximal over suitable finite fields and their full automorphism groups are the Suzuki and Ree groups. In this paper we determine explicit generators of the fixed fields of these full automorphism groups in the corresponding function fields. Motivated by Dickson's classical study of invariants of finite linear groups, we use the natural projective representations of the two groups. In the Suzuki case the proof uses restricted Dickson invariants, whereas in the Ree case it relies on an invariant bilinear form of the seven-dimensional representation.
Related
- Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups
- Ramanujan Conjecture and Riemann Hypothesis for the unitary groups over function fields
- Multiplicator freeness for restricted-ramification Galois groups over global function fields
- Abelian dynamical Galois groups over global function fields
- The inductive Navarro-Alperin weight condition for the Suzuki and Ree groups
BibTeX
@misc{timpanella2026explicit,
title = {{Explicit invariants of the Suzuki and Ree groups in their function fields}},
author = {Marco Timpanella},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15951},
eprint = {2609.15951},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15951},
}
RIS
TY - UNPB
TI - Explicit invariants of the Suzuki and Ree groups in their function fields
AU - Marco Timpanella
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15951
UR - https://arxiv.org/abs/2609.15951
AB - The Suzuki and Ree curves are two classical Deligne--Lusztig curves. They are maximal over suitable finite fields and their full automorphism groups are the Suzuki and Ree groups. In this paper we determine explicit generators of the fixed fields of these full automorphism groups in the corresponding function fields. Motivated by Dickson's classical study of invariants of finite linear groups, we use the natural projective representations of the two groups. In the Suzuki case the proof uses restricted Dickson invariants, whereas in the Ree case it relies on an invariant bilinear form of the seven-dimensional representation.
ER -