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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | 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 |
| Цитувати: | Note on Exponents Associated with Y-Systems. Ryo Takenaka. SIGMA 21 (2025), 028, 21 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862598890084106240 |
|---|---|
| author | Takenaka, Ryo |
| author_facet | Takenaka, Ryo |
| citation_txt | Note on Exponents Associated with Y-Systems. Ryo Takenaka. SIGMA 21 (2025), 028, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T11:59:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213186 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:59:43Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Takenaka, Ryo 2026-02-16T16:35:14Z 2025 Note on Exponents Associated with Y-Systems. Ryo Takenaka. SIGMA 21 (2025), 028, 21 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 17B22; 81R10 arXiv:2410.02286 https://nasplib.isofts.kiev.ua/handle/123456789/213186 https://doi.org/10.3842/SIGMA.2025.028 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). The author would like to thank his supervisor, Masato Okado, for helpful comments and discussion on this research. The author is also grateful to the anonymous referees for their valuable comments and suggestions, which helped to improve the clarity and quality of this paper. JST, the establishment of university fellowships towards the creation of science, technology, and innovation, Grant Number JPMJFS2138, supported the author. This work was partly supported by MEXT Promotion of Distinctive Joint Research Center Program JPMXP0723833165. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Note on Exponents Associated with Y-Systems Article published earlier |
| spellingShingle | Note on Exponents Associated with Y-Systems Takenaka, Ryo |
| title | Note on Exponents Associated with Y-Systems |
| title_full | Note on Exponents Associated with Y-Systems |
| title_fullStr | Note on Exponents Associated with Y-Systems |
| title_full_unstemmed | Note on Exponents Associated with Y-Systems |
| title_short | Note on Exponents Associated with Y-Systems |
| title_sort | note on exponents associated with y-systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213186 |
| work_keys_str_mv | AT takenakaryo noteonexponentsassociatedwithysystems |