The box-ball system is an integrable cellular automaton on one dimensional
lattice. It arises either from quantum as well as classical integrable systems
by the procedures called crystallization and ultradiscretization, respectively.
The double or...

J. Phys. A: Math. Theor. 44 (2011) 135204 Nov 2010

Fermionic formulas in combinatorial Bethe ansatz consist of sums of products
of q-binomial coefficients. There exist refinements without a sum that are
known to yield partition functions of box-ball systems with a prescribed
soliton content. In th...

The T and Y-systems are ubiquitous structures in classical and quantum
integrable systems. They are difference equations having a variety of aspects
related to commuting transfer matrices in solvable lattice models, q-characters
of Kirillov-Reshet...

Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi

Jan 2010

We prove the periodicities of the restricted T and Y-systems associated with
the quantum affine algebra of type C_r, F_4, and G_2 at any level. We also
prove the dilogarithm identities for these Y-systems at any level. Our proof is
based on the tr...

Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi

Jan 2010

We prove the periodicities of the restricted T and Y-systems associated with
the quantum affine algebra of type B_r at any level. We also prove the
dilogarithm identities for the Y-systems of type B_r at any level. Our proof is
based on the tropic...

During the period of research project, we mainly obtained the following results.1. [Affine geometric crystal]In collaboration with M. Kashiwara and T. Nakashima, we constructed geometric crystals associated to nonexceptional affine Lie algebras. W...

Among the systems of discrete equations, quantum mechanical lattice models and Cellular Automata (discrete dynamical systems which take finite number of states), there exist a class of systems named integrable systems in which exact solutions and/...

Significant progress has been made on the one dimensional soliton cellular automata associated with quantum groups and related topics.The results (1)-(6) obtained in the three years are explained herewith.(1) On D type tropical R, its bilinear for...