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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.31478

Authors: Ge, Hong-Jun, Koolen, Jack H., Liu, Jing-Yuan, Yoshino, Kiyoto

Institutions: University of Science and Technology of China, Toho University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214642742

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