Note on Exponents Associated with Y-Systems
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213186 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Note on Exponents Associated with Y-Systems. Ryo Takenaka. SIGMA 21 (2025), 028, 21 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 a quiver derived from the pair (ₙ, ℓ). Mizuno provided conjectured formulas for the exponents associated with Y-systems in [Mizuno Y., SIGMA 16 (2020), 028, 42 pages, arXiv:1812.05863]. In this paper, we study the exponents associated with level 2 Y-systems for classical Dynkin types. As a result, we present proofs of Mizuno's conjecture for (ₙ, 2) and (ₙ, 2), and give a reformulation for (ₙ, 2).
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| ISSN: | 1815-0659 |