Publications

Keywords

Targets  

mathematical physics  >  integrable system  >  Toda lattice,  Mumford system,  Box-ball system, T/Y-system                                  

geometry > hyperbolic geometry > knot invariants, Teichmuller theory

Methods

algebraic/tropical geometry  >  Jacobi variety,  Riemann's theta function                      

quantum group  >  crystal base                                                                                                               

cluster algebra

Preprints

Papers (Since 2000)

Solutions of tetrahedron equation from quantum cluster algebra associated with symmetric butterfly quiver (with Atsuo Kuniba, Xiaoyue Sun, Yuji Terashima and Junya Yagi) SIGMA 20 (2024), 113, 45 pages. arXiv: 2403.08814 

Cluster mutation and 3D integrablity, RIMS Kokyuroku Bessatsu, B96, 1 - 10 (2024).  (in Japanese) 

T-Systems, Y-Systems and Cluster Algebras, Encyclopedia of Mathematical Physics 2nd edition, Volume 3, 239 - 250 (2025).

Quantum cluster algebras and 3D integrability: Tetrahedron and 3D reflection equations (with Atsuo Kuniba and Yuji Terashima) IMRN, rnae128, 11549 - 11581 (2024). arXiv: 2310.14493 

Tetrahedron equation and quantum cluster algebras (with Atsuo Kuniba and Yuji Terashima) J. of Phys. A: Math. Theor., 57, 085202, 33pp (2024). arXiv: 2310.14529 

Invariants of Weyl group action and q-characters of quantum affine algebras (with Takao Yamazaki) Algebras and Representation Theory,　 26, no. 6, 3167 - 3183 (2023).  arXiv: 2207.09867 

Cluster realizations of Weyl groups and q-characters of quantum affine algebras, Lett. Math. Phys., 111, no. 1, 4 (2021).  arXiv: 2003.04491

Cluster realizations of Weyl groups and higher Teichmuller theory (with Tsukasa Ishibashi and Hironori Oya) Selecta Mathematica, 27: 37 (2021). arXiv:1902.02716

Cluster realizations of Weyl groups, RIMS Kokyuroku Bessatsu, B78, 225 - 233 (2020). 

Soliton cellular automata associated with infinite reduced words (with Max Glick and Pavlo Pylyavskyy) Annales de L'Institut Henri Poincare D7, no. 2, pp 249 - 302 (2020).  arXiv:1712.08989

On the cluster nature and quantization of geometric R-matrices (with Thomas Lam and Pavlo Pylyavskyy) Publ. RIMS, 55, pp 25 - 78 (2019). arXiv:1607.00722

Toric networks, geometric R-matrices and generalized discrete Toda lattices (with Thomas Lam and Pavlo Pylyavskyy) Comm. Math. Phys., 347, pp 799 - 855 (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).  nlin/0404047.

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).