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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.07012 |
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Table of Contents:
- We give a generalisation of the Lenstra-Lenstra-Lovász (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group $G$. This can be regarded as `lattice reduction with symmetries'. We make this algorithm explicit for the classical groups $G = \mathrm{Sp}_{2g}$, $\mathrm{SO}_{2g}$, and for the exceptional group $G = G_2$.