T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras

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.

23 pages; the final (journal) version published in SIGMA

References in corpus (5)

• The ODE/IM Correspondence
• Quiver varieties and cluster algebras
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Q-systems as cluster algebras II: Cartan matrix of finite type and the polynomial property
• Perturbed Defects and T-Systems in Conformal Field Theory

Cited by in corpus (2)

• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r
• Periodicities in cluster algebras and dilogarithm identities