Orbits in Lattices
arXiv:2205.10601 · doi:10.1016/j.jnt.2024.06.013
Abstract
We exhibit algorithms for calculating Tits' buildings and orbits of vectors in a lattice for certain subgroups of . We discuss how these algorithms can be applied to understand the configuration of boundary components in the Baily-Borel compactification of orthogonal modular varieties and to improve the performance of computer arithmetic of orthogonal modular forms.
21 pages. Preliminary version