Nakajima quiver varieties, affine crystals and combinatorics of Auslander-Reiten quivers

• Date: 2023
• Main Authors: Kus, D., Schumann, B.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: crystal bases; Kirillov-Reshetikhin crystals; Nakajima's quiver varieties; affine Lie algebras; 81R50; 81R10; 16G20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1952
• Journal Title: Algebra and Discrete Mathematics

We obtain an explicit crystal isomorphism between two realizations of crystal bases of finite dimensional irreducible representations of simple Lie algebras of type \(A\) and \(D\). The first realization we consider is a geometric construction in terms of irreducible components of certain Nakajima q...