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

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

2009-09-25

arxiv.org/abs/0909.4618v3

SIGMA.5:108,2009

Mathematics

Quantum Algebra

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

Scientific paper

10.3842/SIGMA.2009.108

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.

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