Note on Exponents Associated with Y-Systems

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Author: Takenaka, Ryo
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/213186
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Note on Exponents Associated with Y-Systems. Ryo Takenaka. SIGMA 21 (2025), 028, 21 pages

Let (ₙ, ℓ) be the pair consisting of the Dynkin diagram of finite type ₙ and a positive integer ℓ ≥ 2, called the level. Then we obtain the Y-system, which is the set of algebraic relations associated with this pair. Related to the Y-system, a sequence of integers called exponents is defined through...