An LLL algorithm with symmetries
Beth Romano, Jack A. Thorne · International Journal of Number Theory · 2025
We give a generalization of the Lenstra–Lenstra–Lovász (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group [Formula: see text]. This can be regarded as “lattice reduction with symmetries.” We make this algorithm explicit for the classical groups [Formula: see text], [Formula: see text], and for the exceptional group [Formula: see text].