120 citations · 682 across the 30 of their papers we have counts for
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Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n
Atsuo Kuniba, Taichiro Takagi
We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an (n+1)-state cellular automaton descri…
Bethe ansatz and inverse scattering transform in a periodic box-ball system
Atsuo Kuniba, Taichiro Takagi, Akira Takenouchi
We formulate the inverse scattering method for a periodic box-ball system and solve the initial value problem. It is done by a synthesis of the combinatorial Bethe ansa"tze at q=1…
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…
Tropical R and Tau Functions
Atsuo Kuniba, Masato Okado, Taichiro Takagi +1
Tropical R is the birational map that intertwines products of geometric crystals and satisfies the Yang-Baxter equation. We show that the D^{(1)}_n tropical R introduced by the aut…
Geometric Crystal and Tropical R for D^(1)_n
Atsuo Kuniba, Masato Okado, Taichiro Takagi +1
We construct a geometric crystal for the affine Lie algebra D^{(1)}_n in the sense of Berenstein and Kazhdan. Based on a matrix realization including a spectral parameter, we prove…
Combinatorial R matrices for a family of crystals : B^{(1)}_n, D^{(1)}_n, A^{(2)}_{2n} and D^{(2)}_{n+1} cases
Goro Hatayama, Atsuo Kuniba, Masato Okado +1
For coherent families of crystals of affine Lie algebras of type B^{(1)}_n, D^{(1)}_n, A^{(2)}_{2n} and D^{(2)}_{n+1} we describe the combinatorial R matrix using column insertion…