PreprintCC BY 4.0arXiv
Abstract regular polytopes of G2(q) in even characteristic
Abstract
For every even prime power q>2, we explicitly construct a rank five string C-group representation of the Chevalley simple group G2(q) using its natural seven-dimensional matrix representation. We also give a census for the string C-group representations of G2(q) of ranks four and above for every prime power 3 ≤ q ≤ 11; providing computational evidence that rank five string C-group representations of G2(q) are rare and that this construction is exceptional among the currently known examples.
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BibTeX
@misc{chen2026abstract,
title = {{Abstract regular polytopes of $G_2(q)$ in even characteristic}},
author = {Malcolm Hoong Wai Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25004},
eprint = {2609.25004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25004},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Abstract regular polytopes of G_2(q) in even characteristic
AU - Malcolm Hoong Wai Chen
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25004
UR - https://arxiv.org/abs/2609.25004
AB - For every even prime power q>2, we explicitly construct a rank five string C-group representation of the Chevalley simple group G_2(q) using its natural seven-dimensional matrix representation. We also give a census for the string C-group representations of G_2(q) of ranks four and above for every prime power 3 ≤ q ≤ 11; providing computational evidence that rank five string C-group representations of G_2(q) are rare and that this construction is exceptional among the currently known examples.
ER -