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

Atsuo Kuniba ; Tomoki Nakanishi ; Junji Suzuki

Symmetry, integrability and geometry: methods and applications, Tome 5 (2009)

Résumé

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.

Détail

Keywords: T-systems; Y-systems; quantum groups; cluster algebras.

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