3 research outputs found
T-systems, Y-systems, and cluster algebras: Tamely laced case
The T-systems and Y-systems are classes of algebraic relations originally
associated with quantum affine algebras and Yangians. Recently they were
generalized to quantum affinizations of quantum Kac-Moody algebras associated
with a wide class of generalized Cartan matrices which we say tamely laced.
Furthermore, in the simply laced case, and also in the nonsimply laced case of
finite type, they were identified with relations arising from cluster algebras.
In this note we generalize such an identification to any tamely laced Cartan
matrices, especially to the nonsimply laced ones of nonfinite type.Comment: 31 pages, final version to appear in the festschrift volume for
Tetsuji Miwa, "Infinite Analysis 09: New Trends in Quantum Integrable
Systems