Keywords Targets mathematical physics > integrable system > Toda lattice, Mumford system, Box-ball system, T/Y-system knot invariants > complex volume Methodsalgebraic geometry, tropical geometry > Jacobi variety, Riemann's theta function quantum group > crystal base cluster algebra PreprintsOn the cluster nature and quantization of geometric R-matrices (with Thomas Lam and Pavlo Pylyavskyy) arXiv:1607.00722 Papers (2000~) Toric networks, geometric R-matrices and generalized discrete Toda lattices (with Thomas Lam and Pavlo Pylyavskyy) Comm. Math. Phys., Online First (2016). arXiv:1504.03448 Braids, Complex Volume, and Cluster Algebra
(with Kazuhiro Hikami) Algebraic and Geometric Topology, 15, 2175-2194 (2015). arXiv:1304.4776 Braiding Operator via Quantum Cluster Algebra (with Kazuhiro Hikami) J. Phys. A: Math. Theor., 47, 474006 (2014).arXiv:1404.2009 Discrete Painlevé equations from Y-systems (with Andrew N. W. Hone) J. Phys. A: Math. Theor., 47, 474007 (2014). arXiv:1405.5379 Algebraic integrable systems related to spectral curves with automorphisms (with Pol Vanhaecke and Takao Yamazaki) J. Geom. Phys., 87, 198-216 (2015). arXiv:1312.4208 Cluster Algebra and Complex Volume of Once-Punctured Torus Bundles and Two-Bridge Knots (with Kazuhiro Hikami) J. Knot Theory and Its Ramifications, 23, 1450006 [33 pages] (2014). arXiv.1212.6042. Tropical curves and integrable piecewise linear maps (with Shinsuke Iwao) Contemp. Math., 580, pp. 21-39 (2012). arXiv:1111.5771. Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry (with Atsuo Kuniba and Taichiro Takagi) (a review article) J. Phys. A, 45, 073001 (2012). arXiv:1109.5349. Difference equations and cluster algebras I: Poisson bracket for integrable difference equations (with Tomoki Nakanishi) RIMS Kokyuroku Bessatsu, B28, pp 63 - 88 (2011).arXiv:1012.5574. Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2 (with Osamu Iyama, Bernhard Keller, Atsuo Kuniba and Tomoki Nakanishi) Publ. RIMS, 49, pp 43 - 85 (2013). arXiv:1001.1881. Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r (with Osamu Iyama, Bernhard Keller, Atsuo Kuniba and Tomoki Nakanishi) Publ. RIMS, 49, pp 1 - 42 (2013). arXiv:1001.1880. Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice (with Shinsuke Iwao) in "Proceedings of the Infinite Analysis 09: New Trends in Quantum Integrable Systems", eds. B. Feigin, et al., pp. 101 - 116 (World Scientific, 2011). arXiv:1003.0057. Singular fiber of the Mumford system and rational solutions to the KdV hierarchy (with Pol Vanhaecke and Takao Yamazaki) Comm. Pure Appl. Math., 63, Issue 4, pp 508 - 532 (2010). arXiv:0806.2362. Periodicities of T-systems and Y-systems (with Osamu Iyama, Atsuo Kuniba, Tomoyuki Nakanishi and Junji Suzuki) Nagoya Mathematical Journal, 197, pp 59 - 174 (2010). arXiv:0812.0667. Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic (with Tomoyuki Takenawa) RIMS Kokyuroku Bessatsu, B13, pp 175 - 190 (2009). arXiv:0902.0448. A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice (with Tomoyuki Takenawa) Comm. Math. Phys., 289, pp 995 - 1021 (2009).arXiv.0806.3318. Tropical spectral curves and integrable cellular automata (with Tomoyuki Takenawa) Int. Math. Res. Not. IMRN, vol. 2008, rnn019, 27 pages (2008). arXiv.0704.2471. Multi-Hamiltonian structures on Beauville's integrable system and its variant (with Yukiko Konishi) SIGMA Symmetry Integrability Geom. Methods Appl., 3, 007, 16 pages (2007).math-ph/0610048. Jacobian variety and integrable system --- after Mumford, Beauville and Vanhaecke (with Yukiko Konishi and Takao Yamazaki) J. Geom. Phys., 57, pp 815 - 831 (2007).math-ph/0512033. Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system (with Takao Yamazaki) Comm. Math. Phys., 265, pp 699 - 719 (2006).math-ph/0501048. A quantization of box-ball systems (with Atsuo Kuniba and Masato Okado) Rev. Math. Phys., 16, pp 1227 - 1258 (2004).The matrix realization of affine Jacobi varieties and the extended Lotka-Volterra lattice J. Phys. A: Math. Gen., 37, pp 1277 - 1298 (2004).The extended Lotka-Volterra lattice and affine Jacobi varieties of spectral curves J. Math. Phys., 44, pp 338 - 351 (2003).The lattice Toda field theory for simple Lie algebras Contemp. Math., 309, pp 115 - 128 (2002).The lattice Toda filed theory and lattice W algebras for B2 and C2 J. Phys. A: Math. Gen., 35, pp 1013 - 1024 (2002).Symmetry of integrable cellular automaton (with Kazuhiro Hikami) J. Phys. A: Math. Gen., 34, pp 2467 - 2476 (2001).The A_M^{(1)} automata related to crystals of symmetric tensors (with Goro Hatayama, Kazuhiro Hikami, Atsuo Kuniba, Taichiro Takagi and Tetsuji Tokihiro) J. Math. Phys., 42, pp 274 - 308 (2001).The lattice Toda field theory for simple Lie algebras --- Hamiltonian structure and tau-function (with Kazuhiro Hikami) Nucl. Phys. B, 581 [PM], pp 761 - 775 (2000).Supersymmetric extention of the integrable box-ball system (with Kazuhiro Hikami) J. Phys. A: Math. Gen., 33, pp 4081 - 4094 (2000). |

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