272 citations · 1k across the 53 of their papers we have counts for
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Rogers dilogarithms of higher degree and generalized cluster algebras
Tomoki Nakanishi
In connection with generalized cluster algebras we introduce a certain generalization of the celebrated Rogers dilogarithm, which we call the Rogers dilogarithms of higher degree.…
Wonder of sine-Gordon Y-systems
Tomoki Nakanishi, Salvatore Stella
The sine-Gordon Y-systems and the reduced sine-Gordon Y-systems were introduced by Tateo in the 90's in the study of the integrable deformation of conformal field theory by the the…
Note on dilogarithm identities from nilpotent double affine Hecke algebras
Tomoki Nakanishi
Recently Cherednik and Feigin obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series…
Tropicalization method in cluster algebras
Tomoki Nakanishi
This is a brief survey on the recently developing tropicalization method in cluster algebras and its applications to the periodicities of Y-systems and the associated dilogarithm i…
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…
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…