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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 108, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.108 (Mi sigma454) 		 
This article is cited in 8 scientific papers (total in 8 papers)

T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac–Moody Algebras

Atsuo Kunibaa, Tomoki Nakanishib, Junji Suzukic

a Institute of Physics, University of Tokyo, Tokyo, 153-8902, Japan
b Graduate School of Mathematics, Nagoya University, Nagoya, 464-8604, Japan
c Department of Physics, Faculty of Science, Shizuoka University, Ohya, 836, Japan
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DOI: https://doi.org/10.3842/SIGMA.2009.108
Abstract: 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.
Keywords: T-systems; Y-systems; quantum groups; cluster algebras.
Received: October 5, 2009; in final form December 16, 2009; Published online December 19, 2009
Bibliographic databases:
Document Type: Article
MSC: 17B37; 13A99
Language: English
Citation: Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki, “T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac–Moody Algebras”, SIGMA, 5 (2009), 108, 23 pp.
Citation in format AMSBIB
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\by Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
\paper T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac--Moody Algebras
\jour SIGMA
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\vol 5
\papernumber 108
\totalpages 23
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    • This publication is cited in the following 8 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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