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arXiv · 0909.4618

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

Atsuo Kuniba·Tomoki Nakanishi·Junji Suzuki
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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.

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Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki. 2009-12-19. T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras. https://doi.org/10.3842/sigma.2009.108

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