An LLL algorithm with symmetries

Key Points

• The research aims to generalize the LLL lattice-reduction algorithm to account for symmetries in arbitrary reductive groups.
• Developed a generalization of the LLL algorithm.
• Focused on explicit applications for classical and exceptional groups.
• Explored group symmetries in relation to lattice reduction.
• Generalization of the algorithm is valid for split, semisimple reductive groups.
• Specific implementations demonstrated for classical groups.
• Algorithm applicability extended to exceptional groups.