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arXiv · 2408.07012

An LLL algorithm with symmetries

Beth Romano·Jack A. Thorne
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Abstract

We give a generalisation of the Lenstra-Lenstra-Lov\'asz (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 $G = G_2$.

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Beth Romano, Jack A. Thorne. 2024-08-13. An LLL algorithm with symmetries. https://arxiv.org/abs/2408.07012

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