Beth Romano, Jack A. Thorne
Published 2024-08-13Version 1
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 $G = G_2$.
Higher level cusp forms on the exceptional group of type $E_{7}$
Symmetries of the Three Gap Theorem
LLL Algorithm for Lattice Basis Reduction
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