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arXiv · 2609.31478

Irreducible rootless unimodular lattices generated by vectors of norm $3$

Hong-Jun Ge·Jack H. Koolen·Jing-Yuan Liu·Kiyoto Yoshino
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Abstract

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.

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Hong-Jun Ge, Jack H. Koolen, Jing-Yuan Liu, Kiyoto Yoshino. 2026-09-25. Irreducible rootless unimodular lattices generated by vectors of norm $3$. https://arxiv.org/abs/2609.31478

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