Integer quadratic forms and extensions of subsets of linearly independent roots

• Date: 2025
• Main Author: Stekolshchik, Rafael
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: Root system; Cartan matrix; Weyl group; Carater diagram; 17B22; 20F55; 20E45
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2397
• Journal Title: Algebra and Discrete Mathematics

We consider subsets of linearly independent roots in a certain root system \(\varPhi\). Let \(S'\) be such a subset, and let \(S'\) be associated with any Carter diagram \(\Gamma'\). The main question of the paper: what root \(\gamma \in \varPhi\) can be added to \(S'\) so that \...