PreprintCC BY 4.0arXiv
Irreducible rootless unimodular lattices generated by vectors of norm $3$
Abstract
The classical ADE classification implies that E8 is the unique irreducible unimodular Euclidean lattice generated by vectors of norm $2$. In sharp contrast, for every positive integer m, we construct an irreducible odd unimodular lattice of rank 24m and minimum norm $3$ that is generated by its minimal vectors.
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BibTeX
@misc{ge2026irreducible,
title = {{Irreducible rootless unimodular lattices generated by vectors of norm $3$}},
author = {Hong-Jun Ge and Jack H. Koolen and Jing-Yuan Liu and Kiyoto Yoshino},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31478},
eprint = {2609.31478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31478},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Irreducible rootless unimodular lattices generated by vectors of norm $3$
AU - Hong-Jun Ge
AU - Jack H. Koolen
AU - Jing-Yuan Liu
AU - Kiyoto Yoshino
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31478
UR - https://arxiv.org/abs/2609.31478
AB - The classical ADE classification implies that E_8 is the unique irreducible unimodular Euclidean lattice generated by vectors of norm $2$. In sharp contrast, for every positive integer m, we construct an irreducible odd unimodular lattice of rank 24m and minimum norm $3$ that is generated by its minimal vectors.
ER -