Lattice reduction is generalized for arbitrary reductive groups, indicating broader applications in mathematics.
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].
No takes yet. Share an insight, caveat, or question.
Romano et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: