233 citations · 1.5k across the 51 of their papers we have counts for
51 papers
Three -Painlevé equations with affine Weyl group symmetry of type
Hidehito Nagao, Yasuhiko Yamada
Three -Painlevé type equations are derived through degenerations of the -Painlevé equation with affine Weyl group symmetry of type -. The three -Painlevé typ…
Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
Sanefumi Moriyama, Yasuhiko Yamada
We study a quantum (non-commutative) representation of the affine Weyl group mainly of type , where the representation is given by birational actions on two variables $x…
The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
Masatoshi Noumi, Simon Ruijsenaars, Yasuhiko Yamada
The 8-parameter elliptic Sakai difference Painlevé equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent…
Quadrirational Yang-Baxter maps and the elliptic Cremona system
James Atkinson, Yasuhiko Yamada
This paper connects the quadrirational Yang-Baxter maps, which are two-dimensional integrable discrete systems of KdV type, and the elliptic Cremona system, which is a higher analo…
Variations of -Garnier system
Hidehito Nagao, Yasuhiko Yamada
We study several variants of q-Garnier system corresponding to various directions of discrete time evolutions. We also investigate a relation between the -Garnier system and Suz…
An Elliptic Garnier System from Interpolation
Yasuhiko Yamada
Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extens…