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arXiv · 2404.03897

Generalised Checkerboard Lattices

Atsushi Matsuo·Hiroki Shimakura
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Abstract

A series of integral lattices parametrised by integers $k,m,n$ are introduced and investigated, where $n$ is the rank of the lattice, including the root lattices described in a uniform way and unimodular lattices such as the Niemeier lattices of type $A_{24}$ and $D_{24}$. The lattices are characterised by means of a sublattice isomorphic to the root lattice of type $A_{n-1}$. A sufficient condition for existence of an orthogonal $k$-frame of such a lattice is given in terms of symmetric $2$-designs.

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Atsushi Matsuo, Hiroki Shimakura. 2024-04-05. Generalised Checkerboard Lattices. https://arxiv.org/abs/2404.03897

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