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T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras
Інший ID:
2000 Mathematics Subject Classification: 17B37; 13A99
Посилання:
T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras / A. Kuniba, T. Nakanishi, J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 58 назв. — англ.
Підтримка:
It is our great pleasure to thank Professor Tetsuji Miwa on the occasion of his sixtieth birthday for his generous support and continuous interest in our works through many years. We also thank David Hernandez for a valuable comment.
Дата:
2009
Переглядів:
371
Завантажень:
212
Анотація:
The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-systems and establish a relation between T and Y-systems. We also introduce the T and Y-systems associated with a class of cluster algebras, which include the former T and Y-systems of simply laced type as special cases.
