120 citations · 399 across the 27 of their papers we have counts for
28 papers
Cluster realization of Weyl groups and -characters of quantum affine algebras
Rei Inoue
We consider an infinite quiver and a family of periodic quivers for a finite dimensional simple Lie algebra and $m \in \mathbb{…
Cluster realizations of Weyl groups and higher Teichmüller theory
Rei Inoue, Tsukasa Ishibashi, Hironori Oya
For a symmetrizable Kac-Moody Lie algebra , we construct a family of weighted quivers () whose cluster modular group $Γ_{Q_m(\mathfrak{g…
Soliton cellular automata associated with infinite reduced words
Max Glick, Rei Inoue, Pavlo Pylyavskyy
We consider a family of cellular automata associated with infinite reduced elements on the affine symmetric group , which is a tropicalization of the rational ma…
On the cluster nature and quantization of geometric -matrices
Rei Inoue, Thomas Lam, Pavlo Pylyavskyy
We define cluster -matrices as sequences of mutations in triangular grid quivers on a cylinder, and show that the affine geometric -matrix of symmetric power representations…
Toric networks, geometric -matrices and generalized discrete Toda lattices
Rei Inoue, Thomas Lam, Pavlo Pylyavskyy
We use the combinatorics of toric networks and the double affine geometric -matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We constru…
Discrete Painlevé equations from Y-systems
Andrew N. W. Hone, Rei Inoue
We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonl…