65 citations · 330 across the 28 of their papers we have counts for
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Combinatorial Bethe ansatz and ultradiscrete Riemann theta function with rational characteristics
Atsuo Kuniba, Reiho Sakamoto
The U_q(\hat{sl}_2) vertex model at q=0 with periodic boundary condition is an integrable cellular automaton in one-dimension. By the combinatorial Bethe ansatz, the initial value…
Tau functions in combinatorial Bethe ansatz
Atsuo Kuniba, Reiho Sakamoto, Yasuhiko Yamada
We introduce ultradiscrete tau functions associated with rigged configurations for A^{(1)}_n. They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role…
The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function
Atsuo Kuniba, Reiho Sakamoto
Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value pr…
Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
Atsuo Kuniba, Masato Okado, Reiho Sakamoto +2
The Kerov-Kirillov-Reshetikhin (KKR) bijection is the crux in proving fermionic formulas. It is defined by a combinatorial algorithm on rigged configurations and highest paths. We…
Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
Reiho Sakamoto
In proving the Fermionic formulae, combinatorial bijection called the Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a bijection between the set of high…