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

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

Quantum cluster algebras and 3D integrability: Tetrahedron and 3D reflection equations (with Atsuo Kuniba and Yuji Terashima). arXiv: 2310.14493 

Papers (Since 2000)

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).