272 citations · 1k across the 53 of their papers we have counts for
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Difference equations and cluster algebras I: Poisson bracket for integrable difference equations
Rei Inoue, Tomoki Nakanishi
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point…
T-systems and Y-systems in integrable systems
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer m…
Periodicities in cluster algebras and dilogarithm identities
Tomoki Nakanishi
We consider two kinds of periodicities of mutations in cluster algebras. For any sequence of mutations under which exchange matrices are periodic, we define the associated T- and Y…
T-systems, Y-systems, and cluster algebras: Tamely laced case
Tomoki Nakanishi
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 affinizati…
Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2
Rei Inoue, Osamu Iyama, Bernhard Keller +2
We prove the periodicities of the restricted T and Y-systems associated with the quantum affine algebra of type C_r, F_4, and G_2 at any level. We also prove the dilogarithm identi…
Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r
Rei Inoue, Osamu Iyama, Bernhard Keller +2
We prove the periodicities of the restricted T and Y-systems associated with the quantum affine algebra of type B_r at any level. We also prove the dilogarithm identities for the Y…